I get nausea every time I look at the WebCrypto API documentation, so if all you get is confusion, consider yourself lucky.
From what I can tell by reading the W3C Web Cryptography API recommendation of 2017, in particular the §19 Algorithm Overview table, the only difference is that the
AES-KW algorithm of RFC 3394 supports wrapKey/unwrapKey but not encrypt/decrypt.
The intent appears to be that you use wrapKey/unwrapKey when you know the plaintext is itself a short uniform random octet string, but encrypt/decrypt if it has any other structure to its distribution; then if you attempt to use encrypt/decrypt with AES-KW, the API will noisily fail because you might be trying to use it with structured data, which AES-KW is unfit to conceal.
For all other documented encryption schemes, public-key or secret-key, wrapKey/unwrapKey just defers to encrypt/decrypt. So there's no idea of KEM at all, which simultaneously generates a key and encapsulates it for you. One can hope that they will introduce a KEM API in the next version of the specification, since with NIST PQCRYPTO it appears the world is finally, nearly two decades after Shoup introduced the concept, converging on it as the basic way to do public-key encryption.