Special move is the blue card. It's basically a high damaging attack with high ki cost.
Special skill is the green card. It's usually giving you buff or debuff on opponent. Sometimes nullify or counter an attack when used in a right time (depends on the character)
Main ability is activated by pressing your character picture in bottom left corner. The effect may vary. Coul be buff or debuffing your opponent. Sometimes they can pull special move or special skill card or even an ultimate move card.
Ultimate move card is a blue colored card with spikes on the edge of the card. It's also a high damaging card but with less cost than special move (it might change in the futurw but currently it cost 20 ki). It can only pulled once. If you holding one during battle and you swap your current character or activate rising rush it will vanish. So be careful on when you pull it. Also even when the character die.
Note: you can check the effects on the character list. They don't write it as special move card or special skill card they write it as special move arts card, special arts card and ultimate arts card. I don't know why they do that. They should decide to call it move or arts. It can be confusing. And also you can actually check it on the help section in the game if still confused. Good luck.