I don't know if there is a definition or not, but here is what I would do:
If I was putting a strainer for the occasional trash, and maybe there would never be any trash, I'd use a wye strainer. It would be one that I would plan to very seldom if ever have to clean.
If I knew that there would be specific trash that would need cleaning on a regular basis, and variable sized trash such as pipe scale that comes in all sizes, I'd use a basket strainer.
As noted, if the process is not interruptible, I'd use 2 in parallel or more likely a duplex basket strainer.
I'd use a basket only if I had to plan to have to open and clean this one on a regular basis.
But that's just the way I see it.
rmw