Hash types supported by hashcat are categorized. These categories are shown in hashcat's extended help output (-hh). They are somewhat self-explanatory, but contain terms of art that may be unfamiliar.
A database file used “behind the scenes” by a general application (SecureCRT, etc.)
File archives (7-Zip, PKZIP, etc.)
Crypto wallets (Bitcoin, Ethereum, etc.)
MS SQL, MySQL, Oracle, etc.
MS Word, Excel, PDF, etc.
Solarwinds, PeopleSoft, Lotus Notes, etc.
A service reached over the network, rather than the protocol it speaks. FTP, HTTP, SMTP and LDAP servers, web servers such as Apache among them.
Such as ENCsecurity Datavault.
Drupal, Joomla, MediaWiki, PrestaShop, etc.
Django, passlib, Ruby on Rails, etc.
TrueCrypt, VeraCrypt, BitLocker, etc.
Some of these can have multiple underlying algorithms that can be configured by the user in a specific order, so quite a few sub-variants are supported.
Other general Key Derivation Functions (KDFs) - phpass, scrypt, PBKDF2-HMAC, etc.
Telegram, Teamspeak 3, etc.
NetNTLM, IPMI RAKP, Kerberos, SNMPv3, etc.
TOTP (Time-based One-Time Passwords), etc.
General and specialized OSes and their common user hash types, including network equipment, UNIX shadow hash types, etc.
LastPass, 1Password, etc. This includes password-specific DBs on the “back end” of applications and OSes (Apple keychain, Mozilla/Firefox, etc)
Special testing modes that use the plaintext password in place of a hash. Used for debugging and research.
PKCS, SSH, GPG, Java keystore, etc.
Algorithms built to detect accidental change or to spread keys across buckets, rather than to resist an attacker. Checksums such as CRC32 answer whether content has been altered, lost or duplicated, and hashes such as MurmurHash and xxHash exist to be fast.
The authentication secrets of contactless tags and cards. hashcat covers iCLASS and MIFARE Ultralight C.
DES, 3DES, etc. See https://en.wikipedia.org/wiki/Known-plaintext_attack
Multipurpose general unsalted cryptographic hashes - MD5, SHA1, Blake, etc.
Raw (unsalted) hashes used for authentication / HMAC purposes (protecting a secret key). See https://en.wikipedia.org/wiki/HMAC
General hash types that are salted, or iterated/nested (SHA1 of the MD5 of a password, etc.)
The bridged generic hash modes, 73000 and 74000, and the hash recipe mode 4000, where the hash is whatever you described or wrote yourself. No fixed category fits them, because the category depends on what you asked for.