There are a number of backpacking terms that don't seem to lend themselves to a precise and universally agreed upon definition. I think of tarp tents as single-wall tents that evolved from tarps. There are versions without sewn-in floors, but my sense is that they're continuing to evolve such that versions with sewn-in floors are becoming more common.

Indeed, that makes it a "tent", and a better term --- at least for those with the sewn-in floors --- might be "single wall tent". It gets a little more tricky when some tent models have a sewn-in floor as an option.

I don't think many people worry about being precise with the terminology.