Assuming its the same PS4 vs Android. Additional covers let you add attacks to any character. There are 3 colors for each hero and each one can go up to level 5 BUT you can only have 13 covers total (5/5/3, 5/3/5, 4/4/5, etc). You can also increase the total level of the character which gives more HP, more attack power for every color (3 stronger ones and 3 weaker ones) when you match 3 and more attack power for the special attacks.
A sword icon increases the total attack of any move. A shield icon decreases the enemy's attack on you. A fist icon does damage after your turn is over (and can be influenced by swords).
Yes, you have to pick your team every time. The trick is finding synergy and covering as many covers as possible (so every match does bigger damage) and using passive attacks.
Like if Professor X is in the game, you would combine him with 3-star Scarlet Witch and 3-star Black Widow. Scarlet Witch has a passive attack that puts a countdown tile which turns surrounding tiles into purple. When the purples appear, you might get 5 in a row which activates Prof X's passive which actually does 1000's of damage to the enemy, Even if you don't get 5 in a row, if you collect enough purple, you can fire Black Widows purple power which adds green tiles to the board (and you pick where). Of course, you can make more 5 in a rows and get more Prof X auto attacks. When you have enough green, you can use Black Widow's special attack which blows a big hole in the board and dose big damage to the whole enemy team.
If you play your cards right, you can set up many moves in succession (unlike traditional PQ). Most special attacks don't end your turn. Goons/generic characters don't make moves but automatically acquire colors that other characters can use in their attacks.
I play both versions. They're similar, but not quite the same. As AoA says, on the mobile/Steam F2P versions of the game, characters are limited to 13 total covers, so 5/3/5, 5/5/3, 3/5/5, 4/5/5, etc are your coverage patterns.
Console MPQ doesn't have those limitations because there's no F2P mechanic to go "oh gosh darn phooey you pulled a 6th cover you can't use maybe you should spend money on another pull and try to get a cover you CAN use so you can champion the character and redeem that unusable cover for additional rewards." So any character you build, you can build 5/5/5 on the console versions. Also, there's no rarity divisions (which is goofy since they kept the character variants in the console version), so everybody is able to reach the same level cap.
Most of the rest of AoA's commentary here is correct. Only other addendum I've got is that the total character roster is different between the versions, partially because the F2P nature of mobile/Steam is that there are always new characters being released to keep people reaching for their wallets, and the console version did kind of a pro forma attempt at DLC characters, but basically stopped bothering with that at release. So the console roster more or less stops right about where the F2P version introduced 4* characters. Nick Fury and She-Thor are in the game from the 4* tier, I think. Maybe X-Force Wolverine. And that's about it. Anybody released on the freemium game after that isn't in the console version.
But the gameplay mechanics are functionally identical (save for, obviously, mechanics introduced with new characters since the code base split) and the console version has the added bonus of being able to do both local and online multiplayer, where the freemium version pits you against an AI-controlled instance of somebody else's roster.