Both Spider-Ham and Spider-Man Noir, were created as different versions of Spider-Man, specifically Peter Parker. Spider-Ham as comedic cartoon pig, and Spider-Man Noir a gritty pulp detective. The two had no interaction till the Spider-Verse event, but had no significant interactions. They also both appeared in the Ultimate Spider-Man tv series version of the Spider-Verse event, but had no interactions there as well.
Spider-Man: Into the Spider-Verse (2018)
This section is in need of major improvement. Please help improve this article by editing it.
When the Kingpin's Collider brought the two out of their home dimensions and to the one that they become trapped him, Peter Porker and Spider-Man Noir trusting the similarities of their dimensions to the one they are both trapped in, leads them to seek sanctuary at Mary Parker's house, in her Peter's Spider lair, where the two of them meet one another beside Peni Parker. Before Peter B. Parker, Gwen Stacy and Miles Morales joins them in their team up plan to get back home.
The ship rose after the release of Spider-Man: Into the Spider-Verse. Fans will typically ship it as a crack pairing, and enjoy having fun with pairing. Typically drawing the two in more comedic situations or more relaxed one. A rubix cube is involved a lot of the time.
Shippers will often compare the ship to Jessica and Roger Rabbit from the movie Who Framed Roger Rabbit, as that was a movie with a human/anthropomorphic animal relationship. It's also a relationship that has an extreme height difference, as well as similarly opposite personalities.
There are some shippers who are uncomfortable with the animal/human aspect but still like the idea. Many of them instead will ship Noir with his universe's version of John Mulaney, given that John Mulaney voices Spider-Ham in Into the Spider-Verse. This also led to art and manips of John Mulaney stand up bits being said by Spider-Ham.
On AO3, HamNoir is the most written ship for both Spider-Ham and Spider-Man Noir. It's also the third most written ship in the Spider-Man: Into the Spider-Verse tag.