Every attack that isn't a Limit, Item, ally attack, Final auto attack and maybe Cure is a normal hit (Sora's normal melee attacks, Sliding Dash, Aerial Spiral, etc) or a finisher (Explosion, Disaster, Aerial Finish, etc). Finishers are distinguished by usually better damage, ability to kill bosses, higher stun, can't be parried, and some benefitting from Combo Boost/Air Combo Boost. Most of Sora's Action abilities (Sliding Dash, Aerial Dive, Explosion) are contextual, based on your position relative to the enemy (Slide Dash causes Sora to lunge forward and start a string on the ground if he's close enough, Aerial Spiral makes Sora jump up off the ground to attack an enemy in the air. If you have Explosion and Guard Break equipped, Guard Break will go off if you're fighting one enemy, Explosion if multiple are around). With the exception of Master, Sora will alternate between Action Ability finishers (ie you can't do two hit -> Explosion -> Explosion, it will always be two hit ->Guard Break->Explosion or two hit -> Explosion -> normal finisher, but you can influence this).

With no abilities equipped, Sora's default combo string (for ground and air attacks) is two normal hits followed by a finisher. Combo Plus adds one more normal hit onto your ground strings and Air Combo Plus adds one more normal hit onto your air strings. Negative Combo reduces the length of ground and air strings by one hit, while Finishing Plus gives you another finisher on the ground and in the air. You get two Combo Pluses by leveling up Valor, two Air Combo Pluses by leveling up Master, one Finishing Plus from leveling, one Finishing Plus from starting on Critical, one Negative Combo from leveling, one more of each by equipping the appropriate keyblade, and some Forms come with innate Combo Pluses/Air Combo Pluses.

Note magic also has normal and finisher hit variants. For Fire/Blizzard/Thunder as Base (no Drive) Sora, the finishers are slower, but have a larger AoE, deal 50% more damage, and have stronger knockback/launching properties. Magnet is always a finisher and takes you straight to the finisher portion of your string, so for instance, if your string has two finishers normally, using Magnet->Thunder will result in Thunder being a finisher. Reflect's a bit tricky, so I'll explain it with the spell.

On the ground, you're free to switch between physical attacks and magic as you wish, and won't break the string, with one exception (Reflect can't be followed by physical attacks until you have Combo Master). So if your normal combo is one hit three finishers, you can use Thunder->Explosion->Thunder->Fire, and the Fire and second Thunder will both be finishers. Using magic in the air will end the string (save for Final's finishers, which are a bit different) and will never be a finisher.

Combo Boost increases the damage of your ground finishers by (1+number of normal hits in your combo)*10%, and they stack linearly. So with one Combo Boost, a string with four normal hits will increase the finishers power by 50%, and with two Combo Boosts (Decisive Pumpkin) will increase their power by 100%. Combo Boost applies to all finishers in the string, does NOT affect magic finishers that require MP (Fire, Blizzard, etc) or Wisdom's Shot, but affects all others (Explosion, Ripple Drive, Magnet Splash, etc). Air Combo Boost does the same, but for air finishers.

All bosses counter after a certain amount of prodding, and finishers push that counter more than anything (most counter after two). This means you generally want long combos with multiple Combo Boosts/Air Combo Boosts (Decisive Pumpkin and Hero's Crest), in order to inflict the most damage in every opening and generally better DPS than finisher spamming, with the added flexibility of Slide Dash, Flash Step, and the like. Finisher spam can be useful against normal enemies, thanks to their high stun.

In general, air combos are stronger than ground (so you want to be using Hero's Crest and Star Seeker if you plan on using Drives for physical attacks) while ground combos are safer, faster, and incorporate magic better.