Indeed, path has a wide range of meanings from the ephemeral to the well-built. Technically, trail is only slightly less flexible, encompassing both rugged hiking trails and urban, well-built bike trails. However, I think either term conjures up a narrower mental image by default. These connotations probably differ significantly based on the speaker’s dialect and background.
Based on my suburban Midwestern U.S. upbringing, I’d consider a typical path to be an urban park path and a typical trail to be a rural hiking trail – even though I’m intimately familiar with urban bike trails, which are technically shared use paths, and even though I would describe the hiking trail as “a path through the woods”. If I were new to OSM and saw presets for “Path” and “Trail”, I’d assume they apply to these images, respectively:
The more a way differs from one of these stereotypes, the more I’d have to make a judgment call.
Even if, according to some dialects, someone leaving shoeprints in the mud has just forged a new path, I’m not confident that a mapper would know they should map it in the first place, let alone apply the Path preset. We’d probably need a separate preset (labeled “Foot Track” in American English), regardless of whether it comes with one tag or two.
I understand what you’re getting at. It’s kind of like how bikeway encompasses both bike path and bike lane. Unfortunately, path and pathway are almost completely interchangeable. Pathway just places more emphasis on the infrastructure than the routing, much like road versus roadway.