Most definitions found online of 'stropping' refer to 'sharpening on a leather strap'. The word 'strop' itself was originally 'strap'. And most of the definitions refer to barbers' razors being most-often 'stropped' - some of those references go back as far as the early 18th century (1702) at least. Some of the definitions also refer to the application of some type of abrasive compound to the strop, to enhance sharpness and/or polish.
By that standard, I don't think there's a clear distinction between just 'stropping' and 'honing' or 'sharpening'. I associate 'stropping' more with the combination of two things: (1) the edge-trailing technique itself and (2) the usual implication that it's done as the final step in sharpening. I don't really associate it with a particular material used for the job, like leather.
One can strop on almost anything, material-wise. If it produces a noticeable improvement in sharpness, that's all that matters. Sometimes the bare material is enough for that, if it's able to burnish or align a very thin, fine edge, as done on a barber's bare leather strop. But if additional thinning or polish is desired, some compound can be utilized for that.
And I'm a believer that one doesn't actually need a strop to thoroughly refine an edge. I've drifted toward using a medium or fine ceramic rod in lieu of stropping, in my preferences for finishing an edge. I feel it leaves a crisper bite in the edge that I like, while reducing burrs to a point where they're insignificant. So, I believe you can replace a strop with a suitable stone or hone of your preference. Beyond that, if I 'strop' on anything at all, it's most often just a quick pass or two on my jeans or on a bare leather belt. I do that mainly just to clean up the residue & debris left clinging along the edge by the sharpening process.