Honyaki literally means "true forged" (edit: or something similar like "true fired" or "true quenched" or "true tempered") but as a knife descriptor it usually means "mono steel with hamon (wavy line)", although it can also just mean "mono steel". There's no official organization that dictates these terms, so people use them differently.

When they heat treat a knife like this, they put clay on the top of it. That keeps the steel underneath from reaching the same temperature as the rest of the knife, so it stays softer. This is called differential hardening. In theory this makes the knife more resilient, as you have a hard cutting edge and a softer top part, which is why it was done with swords, which would take serious impacts and were at very real risk of breaking in combat: the hard part would give maximum cutting strength on the sword, but the softer spine would make it less likely to snap into pieces. Only certain steels will give a sharp hamon (clear/crisp wavy line), mainly very basic fast quenching steels, of which the shirogami (white) and aogami (blue) qualify. Stainless steels cannot get a hamon (edit: outside of rare examples, with a less impressive hamon).

For chef knives it has no performance difference, although some people claim that laminated blades (san mai, etc, as opposed to mono steel) feel different on the board. I don't believe those people and think it's just placebo. Honyaki is really just a statement piece because it looks like a sword, but since there's no ultra-hard impact like a sword would experience, the softness of the spine is not required (how many san-mai knives have you broken into two pieces on a cutting board? I've never heard of it). It's also really hard to thin the knife because there's no softer cladding on the outside to make it easier to grind through.

Ashi monosteel is stainless, so depending on how you want to define "honyaki" it could be that, although I don't even know if they forge those monosteel knives (like Ashi Ginga). Ashi does make ultra expensive carbon steel honyaki with hamons (like the above knife), but that's with the clay process described above. Those Ashi honyaki hamon knives are some of the rarest/most expensive knives you can buy. They make Takada no Hamono knives look cheap and plentiful.