There are three types I guess. Symmetric, Asymmetric and Hash functions. They all have their own purposes.

Symmetric Algorithms

This is where the same key is used to encrypt and de-crypt.

Asymmetric Algorithms

This is where a public key is used to encrypt and a private key is used to decrypt. The private key is derived from the public key.

Hashing Algorithms

These are one way and non-reversible. These are used for data integrity and password storage

Key Derivation and Password Hashing Functions

Protocols and Algorithm Standards

Protocol Encryption Standard
TLS 1.3 AES-GCM, ChaCha20-Poly1305, X25519, SHA-256
OpenSSH ed25519, X25519, ChaCha20
Signal Protocol X3DH (X25519), AES-GCM, HMAC-SHA256
WireGuard VPN ChaCha20-Poly1305, Curve25519, Blake2s
JWT Tokens RSA/ECDSA, with SHA-256
PGP/GPG RSA, ECC, SHA-256
BitLocker / FileVault AES-128/256