As for mechanics, I don't really have the energy to make a list of all the differences. Maybe someone else can help.
Sigh..that's a lot of work man. What the heck, I'll take a shot at it.
The thing with mechanical differences in 4th edition, is that 90% of class abilities are contained in the power lists for each class, to really understand what makes a class tick, you need to really look over the powers and notice the trends.
It's like comparing spell lists between classes in 3rd edition, and as such there is often exceptions--like how in 3rd edition Clerics generally excell at healing and buffing but still have a small range of blasty or save or die spells. Wizards are still the blasty class compared to Clerics because they generally have access to a much deeper and more versatile selection of blasty spells.
Anyhow, here we go.
Martial Martial is defined by classes who peform exploits through skill, training, and ability. What they do may be strictly impossible by human standards, but is not overtly supernatural. Martial classes rely heavily on the 3 physical stats, but may use one or more mental stats as a secondary.
Martial classes, whatever their primary role, tend towards striker as a secondary role. All the martial classes do good damage even compared to other classes in their role. Martial Classes use weapons exclusively in all their powers, they have no implement powers at all.
Martial Classes have access to a good range of status effects, and even some healing, but they never* (there is one exception) use any powers with elemental keywords, necrotic, radiant, psychic or force damage. They do not have teleport powers, and they do not create zones, summons or conjurations. They may have enhanced leaping, climbing, or shifting abilities, but cannot fly or grant flight to others. Some stealth based powers use the invisibility keyword, primarily for the Rogue.
Because all martial classes use weapons extensively, weapon choice is key for martial characters, and they are by far the most likely classes to invest in weapon specific feats to enhance their powers and fighting skills.
Martial Characters also have a large number of skill based powers, or abilities that require a minimum level of skill in order to use.
Martial Classes have by far the largest number of stance based powers. Stances are powers that provide effects that last the rest of the encounter unless the stance is cancelled, but cannot be stacked with other stances.
Overall, martial classes are much less flashy than the other power sources, and somewhat less versatile in the range of abilities they posess, but are often highly specialized in their role, and very dangerous to the enemy.
Arcane Arcane is the polar opposite of martial in many ways. While martial characters forgo flashiness for solid damage dealing, Arcane is easily the flashiest and most unpredictable power source.
Arcane characters can gain their power through diverse means, whether they gain their powers by study, dangerous pacts with sinister powers, or harnessing the power inherent to their blood, the arcane power source
Whatever their primary role, Arcane Classes lean towards controller as a secondary role. Compared to other classes in their role, arcane characters have large numbers of aoe attacks and negative status effects.
Arcane classes have probably the largest variety of keywords, as technically almost anything is possible for them. They are especially fond of elemental powers, and have a decent number of relatively rare keywords such as poison, necrotic, and acid damage.
Where Arcane classes really dominate though, is their access to Fire, Cold, Psychic, Force, Teleportation, and Illusion powers. Force, Teleportation and Illusion particularly as almost the exclusive domain of arcane classes, while jedi mind tricks and fire or cold based explosions are just something they have even more of than other power sources that are good at the same thing.
Overall, Arcane classes love combining base trickery with big explosions, preferably while teleporting someone into said explosion.
Arcane classes also make extensive use of conjurations, summons, and zones, and make good use of invisibility and flight as well.
Although a few arcane characters can use weapon powers, all arcane classes can and do use implements as well. In some cases (Wizard staffs, sorcerer daggers, swordmage swords) they use special weapons that can also act as implements. The wand in particular can be used by almost all arcane classes, and is a good choice for arcane dabblers and half-elves.
Arcane characters focus heavily on mental stats, paticularly Intelligence and Charisma, with Con being the most used physical stat.
Divine
Divine Classes are generally ordained with divine powers in order to serve the god they worship. Whatever their primary role, divine classes tend to lean towards leader as a secondary role, with the largest number of powers useful for healing and bolstering allies.
The primary implement for Divine Characters is the Holy Symbol, which is unique in that it does not have to be held in order to be used, making it easier for Divine Characters to make use of weapons and sheilds compared to Arcane or Primal Characters. The one exception is the Invoker, who forgoes the holy symbol in favor of Staves and Rods, carried by the Invoker as a symbol of divine authority.
All Divine Classes have the Channel Divinity Encounter power, which allows them to channel divine energy into a number of minor effects, or to smite the undead. Feats can be used to expand Channel Divinity with God specific powers.
Like Arcane, Divine Characters are much more flashy than martial characters, however their range of powers tend to be much more focused. Divine Powers make massive use of Radiant Damage compared to any other power source, for both attack and defense. It is almost possible to make a character of any divine class who uses nothing but radiant damage.
When not bursting with Divine Radiance, Divine characters most often make use of Thunder, Fear and Psychic Damage. Fear and Psychic are almost always paired, in a "bow down before your god" sort of way, possibly while a thunderclap rumbles overhead.
Fire also gets a fair bit of use, and Invokers like to toss in a bit of lightning from time to time as well.
As most divine characters carry weapons, many of their powers inflict weapon damage as well, but channeling radiant or thunder damage through weapon strikes is a popular way of smiting heretics for any divine character.
Cold, Poison, Necrotic, and Force Damage are almost unheard of among Divinely granted powers.
Divine Characters make good use of Zones and Conjurations, although these are often defensive in nature. They have more teleporation powers than Primal or Martial characters, but still far less than Arcane.
As mentioned above, Divine Characters make extensive use of healing and buffing effects, and Clerics stand out as the best healers in the game.
Wisdom and Charisma are the key stats for most divine classes, with Strength and Intelligence the second most common stats.
In general, Divine Classes stand out in their power against the undead, and their ability to support allies, but they aren't usually known for their massive damage potential, either with weapons or implements.
Primal is the 4th one, but it's harder, so I'm taking a break. I might add it later if there is any interest.
Your mechanical differences stem from the nature of spells themselves, rather than the spell in question. It's a fair point, but not relevant to all levels of play.
