a public key (like your account number, which you can share to receive funds)
Considering that in Bitcoin and a lot of altcoins that copied the concept from Bitcoin, there is no such thing as "account number" calling public key that makes little sense.
Public key is just the public part of the duo that can be shared but in cryptocurrencies like Bitcoin, you don't share that. Instead you share your address that is computed using the public key.
The private key makes use of an alphanumeric string
A private key is just a big number (in almost all coins it is 256-bit) and that big integer can be encoded any way you like. In Bitcoin it is usually encoded using Base58 but you can encode it using any other algorithm yourself. For example here is a random private key encoded using BIP39 word list:
L1ejLLY7ixNwU1CrPtERLh8ZhXeskuJRNMwgZBPDbsqxuF5Ba1X2
loud series illness stereo ceiling gun define endless mechanic negative drop april junior half build quit strike shell ill dumb empower surface crawl cable
A seed phrase (also called a recovery phrase) is a group of 12 or 24 random words
It is worth knowing 12 or 24 are the most common number of words in a mnemonic. However depending on the algorithm, it can be any number.