all types of chain?

There's only one Chain — Riftbound doesn't have "types" of chains. Rule 330.1: only one Chain can exist at a time, and any new card or ability played while it exists gets added to that same chain (330.2).

What does have categories is the items on it. Every chain item is either Pending or Finalized: it's added as a Pending Item and becomes Finalized after the Check Legality step of playing it (Rule 329). Items that can sit on the chain are cards (units, gear, spells), tokens, and abilities — activated, triggered, and reflexive (Rules 328.1, 388).

One practical split worth knowing: permanents (units and non-unit gear) leave the chain when finalized and hit the board immediately (Rule 359.2), while spells linger on the chain as Finalized items until they resolve (359.3). Everything resolves last-in-first-out (Rule 340.1).