check is defined...
SKILL CHECKS
A skill check takes into account a character’s training (skill rank),
natural talent (ability modifier), and luck (the die roll). It may also
take into account his or her race’s knack for doing certain things
(racial bonus) or what armor he or she is wearing (armor check
penalty), or a certain feat the character possesses, among other
things. For instance, a character who has the Skill Focus feat (page
100) related to a certain skill gets a +3 bonus on all checks involving
that skill.
To make a skill check, roll 1d20 and add your character’s skill
modifier for that skill. The skill modifier incorporates the character’s
ranks in that skill and the ability modifier for that skill’s key ability,
plus any other miscellaneous modifiers that may apply, including
racial bonuses and armor check penalties. The higher the result, the
better. Unlike with attack rolls and saving throws, a natural roll of
20 on the d20 is not an automatic success, and a natural roll of 1 is
not an automatic failure.
ABILITY CHECK
The Ability Check is one of three types of d20
Tests. The rules often call for an Ability Check,
and the DM can also call for an Ability Check,
determining which ability to use when a creature
attempts something (other than an Attack Roll or
a Saving Throw) that has a chance of meaningful
failure. When the outcome is uncertain and
narratively interesting, the dice determine the
results.
The Ability Check has the following special
rules.
SKILLS
When you make an Ability Check, the rules or the
DM determines whether a Skill Proficiency is
relevant to the check. If you have a relevant Skill
Proficiency, you can add your Proficiency Bonus
to the roll. For example, if a rule refers to a
Strength Check (Acrobatics or Athletics), you can
add your Proficiency Bonus to the check if you
have Acrobatics or Athletics Proficiency.
ACTION REQUIRED
Making an Ability Check requires you to take an
Action unless a rule says otherwise. Several of
the named Actions—such as Hide and
Influence—include Ability Checks.
The DM may override this requirement and
allow a particular Ability Check to be made as
part of a Bonus Action or as no Action at all.
DIFFICULTY CLASS
The DM determines the Difficulty Class of an
Ability Check and can override a DC specified in
the rules. The Typical Difficulty Class table
shows the most common DCs.
The default DC for a check is 15, and it is rarely
worth calling for an Ability Check if the DC is as
low as 5, unless the potential failure is
narratively interesting.
TYPICAL DIFFICULTY CLASS
Task Difficulty DC
Very Easy 5
Easy 10
Medium 15
Hard 20
Very Hard 25
Nearly Impossible 30
ABILITY CHECK
The Ability Check is one of three types of d20
Tests. The rules often call for an Ability Check,
and the DM can also call for an Ability Check,
determining which ability to use when a creature
attempts something (other than an Attack Roll or
a Saving Throw) that has a chance of meaningful
failure. When the outcome is uncertain and
narratively interesting, the dice determine the
results.
The Ability Check has the following special
rules.
SKILLS
When you make an Ability Check, the rules or the
DM determines whether a Skill Proficiency is
relevant to the check. If you have a relevant Skill
Proficiency, you can add your Proficiency Bonus
to the roll. For example, if a rule refers to a
Strength Check (Acrobatics or Athletics), you can
add your Proficiency Bonus to the check if you
have Acrobatics or Athletics Proficiency.
ACTION REQUIRED
Making an Ability Check requires you to take an
Action unless a rule says otherwise. Several of
the named Actions—such as Hide and
Influence—include Ability Checks.
The DM may override this requirement and
allow a particular Ability Check to be made as
part of a Bonus Action or as no Action at all.
DIFFICULTY CLASS
The DM determines the Difficulty Class of an
Ability Check and can override a DC specified in
the rules. The Typical Difficulty Class table
shows the most common DCs.
The default DC for a check is 15, and it is rarely
worth calling for an Ability Check if the DC is as
low as 5, unless the potential failure is
narratively interesting.
TYPICAL DIFFICULTY CLASS
Task Difficulty DC
Very Easy 5
Easy 10
Medium 15
Hard 20
Very Hard 25
Nearly Impossible 30
and your attempt to redefine it as a mere requirement of slot level is entirely unreasonable.
I'm not redefining it, I'm stating under which circumstances counterspell IS an ability check. If you sacrifice a sufficient level spell, you evoid the ability check.
But, as stated, counterspelling a spell of higher level than the one the opponent cast requires an ability check (such as if the opponent casts a 5th level spell but I cast counterspell at 3rd level). You add your spellcasting ability modifier. Bards, if they grab counterspell, get to add jack of all trades, abjurers get to add their proficiency bonus.
This is either flat wrong or a stellar example of the painful splitting of hairs caused by "natural language" frequently robs GMs of the ability to convey clear & concise meaning with clear & concise wording. Checks are a term that is fairly well accepted as a specific thing throughout the ttrpg community and nearly every editionof d&d other than 5e. Thanks to natural language and a lack of well defined terms we need to hash out if some form of check like a skill check with a d20 roll is meaningfully different from a logic flow gating where counters Pell needs to be cast at the same slot level or higher. Luckily 6e is already improving this gm kneecap ping self inflicted wound with "d20 checks" as a specifically defined subset of "d20 tests.
With that basic terminology settled we can avoid a long winding discussion over If the meaning of defined terms is a subjective matter of personal opinion or not and just move on to why you rarely saw players counterspell in 3.x but see it regularly in 5e. On the topic of how often conterspell is used now vrs then, it shouldn't be ignored that counterspell in 5e went from a specific readied action to a playloop violating retcon reaction that does not even cost an action† to nullify an opponent's action. Of course removing questions like "do I think they will cast a spell?" and "do I think that the spell they are going to cast is worth burning my action to maybe counter?" is going to dramatically lower the bar for counterspell to be cast regularly.
This thread has been filled with statements about how the gm should telegraph things more to support the desires of a player who didn't notice "sufficient telegraphing" prior to step2 in the playloop to avoid locking in fiction resolved by completed rolls that have already been made & tallied during step3 of the play loop in case a player uses a reaction ability to retcon them outside of their turn in step3... Perhaps your observation of counterspell nonuse is on you simply failing to "sufficiently telegraph" thingds like dangerous casters during steps 1 & 3 the GM is responsible for? Many experienced GMs do that by sprinkling in phrases like "lord bbeg is a skilled and dangerous wizard/sorcerer, be on your guard for his signature $spell" and in combat actions with phrases like " the lich looks like it's gearing up to cast another spell after laying down that wall/web/etc spell it just dropped" where & when appropriate. Alternately, perhaps you did that kind of thing & your players simply did not often feel that counterspelling a spellcaster as a matter of reflex to be worth the opportunity cost of a readied action as often as it is in 5e given how far the bar has been lowered. I thought that quoting the whole entry in a for the old counterspell would make the rule "sufficiently telegraphed" rand avoid drawing exclusively on everyone's memories. spoiler (which you also quoted) so "You do this by choosing the ready action (page 160). In doing so, you elect to wait to complete your action until your opponent tries to cast a spell." is already established as a "sufficiently telegraphed" thing rather than a thing we need to make an effort to recall. 5e's counterspell has no such check or readied action requirement
* Before anyone asks why I left out counterspell in 2e. It may have been in a splatbook/supplement of some form but my memory along with the phb & dmg don't appear to have any counterspelling other than some specific spells saying they counter each other,
†"reaction" may be a type of action but it is not an "action", natural language strikes again
Yes, the 3e mechanic for counterspell was perfect for ensuring it rarely (as far as I saw, never) got used. Whether that's good or bad and whether that's better than 5e which does allow too much counterspell splatting (though it's actually more limited then many realize) is better for another thread.