Types of clauses
I’m afraid that identifying types of clauses is much like identifying parts of speech. It depends who’s doing the analysis and what purpose they plan to put that to just which ones you get.
Once you split between dependent and independent clauses, or clauses that stand in for another part of speech like noun, adjective, or adverb, the entire thing becomes as much fun as counting angels dancing on pinheads.
That’s why you find various mention of adjective clauses, concessive clauses, free relative clauses, manner clauses, reinforcement clauses, counterfactual conditional clauses, adverbial clauses, nonfinite relative clauses, integrated relative clauses, time adverb clauses, participle clauses, reduced relative clauses, embedded clauses, nonfinite clauses, noun clauses, verb-first clauses, time clauses, gerund clauses, elliptical clauses, matrix clauses, content clauses, purpose clauses, cause clauses, bear clawses, nonrestrictive relative clauses, dependent clauses, difficult-to-classify clauses, correlative clauses, subordinate clauses, exclamative clauses, contrast clauses, to-infinitive clauses, finite clauses, condition clauses, restrictive relative clauses, factual conditional clauses, nominal relative clauses, argument clauses, addition clauses, apposition clauses, defining clauses, place adverb clauses, santa clauses, result clauses, concession clauses, summary clauses, adjunct clauses, reason clauses, conditional clauses, nominal -ing clauses, independent clauses, predicative clauses, small clauses, place clauses, and Wh-clauses.
It gets exhausting after a while, and that list isn’t even exhaustive. Just imagine it if were!