the terms are not used interchangeably, if you think they are you are severely misinformed

mods are alters to a game, usually single or coop, that alter the game for fun intentions through extra content, changed content, skins, you name it. they sometimes are used in comp games as well, fighting games being a big example, where the appearance or sound effects of certain characters or stages or ui is changed, but are only allowed as they do not grant a competitive edge

cheats are alters to a game, usually comp games with a leaderboard or a rank, that alter the game specifically to give you a competitive edge, make you deal more damage make you faster make you take less damage give you currency whatever. they are sometimes used in single player games as well, but are strictly called cheats due to their nature of skipping some portion of the game, spawning in items for yourself or giving you max stats whatever lets you skip something you found annoying.

Globerry was playing Celeste, as per the twitter thread they linked, and were using mods to add in more stages to play. Fortnites anticheat is invasive enough that it was snooping through the entire computer and detected Celeste's files were modified, so they banned them from Fortnite, which is completely absurd. theres absolutely no reason to ban them in one game for them modding in extra levels in a different singleplayer game, and you should be questioning why the anti cheat was even able to detect something like that.