This question was asked at chia_network.public on Keybase.
These schemes are from the BLS spec in the IETF. AugSchemeMPL, which is what Chia uses, is more secure, but less efficient. PopSchemeMPL is secure, but it requires registration, for example with Ethereum 2.0 Proof of Stake. BasicSchemeMPL is very fast, but not as secure.