In my campaign/headspace, [Force] is "pure magic". It is unassociated with any element, and ironically has no "force" associated with it (unless given that by something). So a magic missile is a bolt of pure energy that "harms" a target, perhaps by directly snuffing its animating energy (life) -- which is why it has no effect on objects. Eldritch blast has no impact... but the Warlock can enhance the bolts with an Invocation that layers in some concussion. A wall of force is simply impassable hardened magic - which does no damage to you, pushing on it, nor can you damage it.
A "blade" formed of "pure magic", though, shouldn't do [Force] damage... it would do [Magical Slash] damage, with an impossibly-sharp edge that slides between molecules (sci-fi). A spiritual hammer should do [Magical Bludgeon], but a spiritual trident would be [Magical Pierce]... magical, but not [Force].
When I took the time to implement side effects for every damage type (applied on Critical Hits, and "exceptional hits" [hit by 10+, or matched d20s when rolling more than 1 for any reason]), [Force]'s side effect wasn't push/pull/concussion; it was "supercharged"! The target became saturated with magical energy and acted like a lightning rod: Disadvantage on its next saving throw against any magically-caused effect (or Advantage on the next spell attack)! It made a nice one-two punch (occasionally) between the Warlock and Druid, with an eldritch blast crit-fishing, then the druid following up a guiding bolt.
[Thunder] is "sonic" and "concussion". If something has "impact" damage or effects, that's [Thunder]. Grenades and other explosives are usually [Fire] and [Thunder], by this definition in my world.
As for the OP... I also headcanon [Psychic] as brain-fry and/or emotional-trauma... anything that might "erode the target's will to fight or hold on". A recent cantrip on reddit called eyesore, for example: it makes the target hideous to his allies... no damage to the target, but allies take psychic damage if they end their turn near the target or try to include it in a spell. They are so disgusted that it "erodes their will to fight" (i guess they want to run off and rinse their eyes or take a bath or something). Mind spike, on the other hand, is just straight-up frying synapses. Do I want to distinguish between them... no-ish? I think the RARE occasions i might want to call out a unique perspective, as the DM, I simply will. "Gargan'k-tk'sh-l 's mind is so foreign that your spell just can't really affect it properly." (But then, I probably would use that same explanation for both "brain-fry" and "emotion", so just "Psychic Resistance" is fine.) UNLESS for some reason I wanted a campaign-unique/specific variant of a monster - like "undead are all animated not by magic, but by magically tying a spirit of some kind to the corpse... as such, weaker under are vulnerable to spells that target the 'spirit', but not those that target the 'mind'. " (or some such)
Related but different topic that someone brought up on an earlier page: "What if we had variations on resistance, like Lesser Resistance, or Greater Resistance?" You mean, like... all previous editions? You could have Fire Resistance 5 and stand comfortably in a campfire all day, but still die in a fireball. Or Fire Resistant 30 - functionally immune to Fire damage, but Ashardalon's breath is still going to cook you (as will bathing in lava). It also made a nice "upcasting" distinction between a level 1 resist elements spell (5pts), a level 2 (10-20 pts, depending on limitations), and a strong level 4 spell (30pts or even "immune... up to 120 total damage"). Not that I don't like "half damage, no matter what" as a concept, too... I just think both can exist, and have value in the system. [And say hello to Heavy Armor Master, which provides a flat DR... which is the same concept!]
As it happens, home rule in my game, Resistance provides a tiny "threshhold" of immunity equal to your PB. If you take damage of a type you resist, up to your threshhold... you take nothing. If you take more, it's just half, no minuses. For example, a level 5 tielfling (PB+3) simply ignores flames of 3pts or less... but if he takes 4 fire damage, it is halved to 2 per the normal rules. This also provides a nice baseline for "what if you have the same resistance from multiple sources?" Double the threshhold! (rather than "no benefit" which is RAW, or "halved again" - i.e. 1/4 damage - which is common at a lot of tables)