No 'garage' is also a music genre. I'm not into music really (certainly not that kind) but I think it's in some way related to but to mark distinction from 'house'.
Of course funnily enough 'the house band' could also be a thing, but neither is related to the genre of that name.
Edit: oh, seems it's a UK thing, so perhaps you weren't to know - https://en.m.wikipedia.org/wiki/UK_garage. Though also older 'garage rock' (60s) on the disambiguation page.
In the US “house” usually refers to the venue - house wine, house band, etc means that supplied by the hotel. You rent a ballroom, you want a band, the hotel can provide the house version, kind of generic.
"Garage band" to me says an outfit so far from being successful that they can't afford rehearsal space, transport to get to one, etc