When and how does bitcoin node sync itself? When does bitcoin node sync itself?

Do different types of sync in bitcoin exist (initial, periodic...)?
Always.

When starting up, Bitcoin Core sends out a request to its peers to inform it about the best chains they know about (using a getheaders message). 

After that point, it is automatic: peers will immediately announce new blocks they knew about after they learn about them. This either happens using:


legacy inv mechanism, in which case just block hashes are announced
BIP130 (if negotiated), in which case announcements send full block headers
BIP152 high-bandwidth mode (if negotiated), in which case blocks are immediately transferred in full using compact blocks protocol