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As I recall, the odour of faeces involves H2S, lower mercaptans, related sufur compounds, heterocyclics like skatole, indole, and variants on that molecular theme. (Putrescine and cadaverine are diamines originating from rotting corpses.) Such molecules can originate from other enzymatic degradations of proteins, and fat degradation also gives particular contributions to the odour. Faecal aromas can originate from rotting tissue, and some fungi and plants produce similar faecal odours, to attract certain insects for pollination and spore distribution. The smell of faeces (as for all aromas) comes from molecules entering the olfactory apparatus in the nose. The molecules locate onto particular sites of the protein surfaces, to send particular electrical signals via the neurones to the brain. That is the "smell", which occurs in the brain.

As odour is caused by volatile molecules, you do not need a solid particle to experience it. Of course, the volatiles are issued from the faecal surface, but a faecal aroma does not necessarily mean a faecal mass or particle. But it usually does, although not always, as shown by my comments about plants and fungi. In particular, a faecal aroma does not necessarily indicate the presence of an infectious material.

It is a common misconception that flatus (fart vapour, if you insist) contains actual, presumably infectious, and certainly noxious, particles of faeces in the air - just one of the myriadof instances of scientific ignorance. It's just that the general public has an imperfect conception of molecular reality.

As an aside, my observation is that, in general discourse, these days, if the speaker has a choice between the words poop or poo, rather than faeces, stools, dung, ordure, droppings, scat, manure, and such-like, they will go for the former, every time! That's especially true of ABC announcers, even in science shows. I wonder why that is. By the way, did you know that the singular of faeces is faex?