Everyone can buy a public cheat, its either open entirely, slotted or some require you to submit a form of identification
A private cheat is limited to friends of the dev or people they invite
There are many cheats that claim to be private but arent, so keep that in mind. The term 'private' is often used to lure unknowing new cheaters into a false sense of security, sometimes leading them to get scammed
There are also some cheats that id consider public but some people have a different opinion (doesnt really matter tho), mainly helite and zerohook. They are slotted but to get a slot you need to go through an application (or get a vouch from an active user, like in a private)
Theyre public because anyone can get in with a bit of patience and determination
A cheat doesnt stay UD for longer just because its private, it can help tho since depending on the cheat you can be sure that noone rages on it meaning there are less bans. A private usually also has less users, just like a slotted product
Also, if a private gets to a certain size but doesnt strictly limits invites it basically turns into a public cheat. Not really a 'problem' for eft but it happens with other games like csgo
TLDR; It doesnt matter whether or not your cheat is private, public or anything in between, just watch out for scammers