Does RSASSAPSS use RSA signature

I just need to know is it correct to classify the RSASSAPSS scheme and sha[256 | 512 | 1]WithRSAEncryption all under RSA signature?

• The CMS standards are not controlling for TLS certificates; TLS standards refer directly to PKIX, in this case (PSS) 4055 updating 3279. Although sha1 sha256 sha512 are the most-used hashes for SSA-v1_5, the other sha2's from 3447+ are presumably allowed, though now I look I don't see an explicit adoption; I'm sure I've seen sha384withRSA used but don't recall the others. (3279 also allowed md2 and md5, but they are now broken.) – dave_thompson_085 Dec 16 '18 at 8:31
• sha256WithRSAEncryption is indeed a signature algorithm. Poor name, if you ask. But that's official. – fgrieu Dec 20 '18 at 13:12