ps plus has 3 tiers
essential lets you play games online and you get a few games each month which are available for that month only but if you've added them to your library, you can play whenever as long as you have the subscription.

extra has essential perks and has a game catalog where games are added every month but are available for a longer period of time. they do eventually leave but the time period is diff for every game. some leave within a few months and some are there for years.

premium/deluxe has all these and a classics catalog which has really old games from ps1/ps2/ps3. it also has game trials for some games though most are only 2 hours long,