Inference is what you do with the model. It's not an executable, so you don't run a model directly, instead a separate program runs and that program reads from the model. Also, hosting can be used to mean running inference on a model, but it could also be used to mean just storing the files and possibly making them available for download, so it's a bit more vague.
Inference sounds cooler and more mystical. Any old company can host something, "running inference" requires 10x rock star engineers and a CEO that acts like a badass who wears a leather jacket and has Thoughts about demographics.
That's interesting, the idea that hosting implies a front-end (whether UI or API).
So it's similar to why we don't call Heroku or Vercel "hosting" or "compute" because it's more of a service (though "cloud" and "platform" are pretty vague too).
When you run a compiler, do you "host" it, or do you run it? Inference is the lingo in the ML world for running input through a model to get some output, where that execution occurs is irrelevant to the idea of inference itself.
If you have a hosted compiler service and you compiled a program with it, you wouldn't say you "compiler hosted" the source code, no, you still "compiled the source code". In the same way, with ML, if it's hosted or local when you run input through the model you performed "inference", that is the act that has occurred (we can debate the term "inference", but "model hosting" is a worse term).
You’d host the model so it’s available to be used.
You’d request it to infer when you wanted to use the model for its purpose.
I'd say "hosting" means making something available to you in the cloud. Model makers don't offer that.
They sell "inference," which is a compute task with real hardware costs for them. The task runs against their model, which is not hosted for you.
So it's similar to why we don't call Heroku or Vercel "hosting" or "compute" because it's more of a service (though "cloud" and "platform" are pretty vague too).
If you have a hosted compiler service and you compiled a program with it, you wouldn't say you "compiler hosted" the source code, no, you still "compiled the source code". In the same way, with ML, if it's hosted or local when you run input through the model you performed "inference", that is the act that has occurred (we can debate the term "inference", but "model hosting" is a worse term).