This page is meant to serve as an explination for the mechanics of Flick Club, but throughout I'm going to be using Yoshi's Cookie (snes) as a point of refrence, so if you're unfamiliar with that game maybe check out how that works
In general, flick club is faster. Everything is at least a few frames faster, and shifting tiles is nearly if not actually instant. Making chains works the same, but the reward you get is different. In yoshi's cookie you get 5 YoCos for a chain, letting you attack right away afterwards and making chains very important for aggressive playstyles. In Flick Club you get 1 toni coin (aka ToCo), flick club's version of a yoshi cookie, per chain. This makes chains way less important since they're not actually that much more efficient than just doing 2 5 clears (the difference in terms of time is also pretty slight, it's in the single digits of frames although that's not really much different than in YoCo). The nature of attacks is also different. In Flick Club there are only 2 non-point attacks (tho the game is currently unfinished so this is likely to change), Freeze and Blind. Blind is basically the same as in Yoshi Cookie (it lasts for ~7 seconds which is how long a blind lasts in a mario mirror in YoCo), freeze works like frozen blocks in Crossniq+, a frozen block cannot be moved at all, making it harder to form chains with pieces that share a row/column with the frozen piece. Point specials also only come in +/-3, no +/-7s. Also there is an all+3 special which gives both sides 3 points. Selecting attacks is not random, instead each player has a hand of cards and making non-ToCo clears will change which card is selected for both players. You can use this to stop your opponent from getting off a good special or to try and select your perfered special. Character differences basically don't exist in Flick Club. Strictly speaking the characters are different as each has a unique turn on and turn off which are suits that will always be good or bad respectively, but statistically each character has the same chance of seeing everything. The turn ons/offs do create unique matchups tho as sometimes one player's turn on is another's turn off, so character choice does matter somewhat, but not in the same way (also, the characters are different sizes and some can obscure your own board, there aren't any cases where it's a big deal but if you want to get really technical about it then Mimi obscures the most, then Zeta, then Skye, then Erin making Erin and Skye the strongest characters). Lastly, in Flick Club you can set weather the winner or loser takes off their clothes, or turn off the stripping altogether, while in Yoshi's cookie you have no control over how clothed any of the characters are. This doesn't effect the mechanics of the game in anyway, but it's a nice accessability option for players that dislike Yoshi's Cookie due to it's ever present nudity with Yoshi and Bowser.
Also, netplay for YoCo must be done via SNES emulation and then fightcade or mednefan or some shit like that. Flick Club has no netplay whatsoever at the moment, so the only way to netplay it is to use parsec or steam remote play. If you want to try steam remote play you'll need a game that has remote play enabled and that you don't give a shit about. I use brawlhalla because it's a free game that everyone I know hates and I think it's funny to send them invites to play it, but you can go with anything, it doesn't matter. Once that's downloaded go into the steam folder for your game (C:/program files/steam/steamapps/game) and take note of the EXE name, rename flickclub.exe to whatever your game's is (for example "brawlhalla.exe") and then delete everything in the steam folder and replace it with everything from the flick club folder. Now start the game from steam and it should boot up flick club instead, but steam thinks it's brawlhalla (or whatever game you used) so you can send an invite to your friend to remote play it. This will also work for any other exe you want to remote play.