Here I'll answer according to my experience and from various reference.
What you mean House is basically Classic House,Chicago House or Jackin House, It's kind of father of all four on the floor genre. The sound characteristics are thicker than garage or disco.
Chicago House gets its name from an actual Disco club called the Warehouse.
If you say Garage and House used interchangeably nowadays, It's true. Because both genres has the grey areas. Simply, don't look at genres as a fixed label. Try to look it as a gradient or heatmap as what towards what.
Garage is the true successor to Disco, without much deviation in form, content, or style. In my opinion, It characterized with groove and light Bassdrum.
The word Garage doesn't mean anything pertinent other than its name comes from the legendary Paradise Garage nightclub in New York City where DJ Larry Levan would play anything he damn well pleased. Garage music simply meant music that Larry played;
In UK scene, there's a broad kind of garage, including
- 2 Step Garage
- Speed Garage
- And even Dubstep born from from this
Most people just name it UK garage, mostly referring to speed garage and 2step garage combined.
Speed garage, A.K.A Bassline House, Bass House, House Garage, Is a derivative of UK garage. mostly focus on bass, yet preserve the groove.
Speed Garage differs from regular Garage in its affections for Jamaican culture and cliches. Not actual Jamaica, of course, but Jamaican transplants in England (this is a UK genre, after all).
Many of my references I get from This link. I think right now it's one of the most comprehensive EDM guide on the net.
Another one would be This genre map