"Business", "commerce" and "trade" are similar but not exactly the same. People don't usually say they are in commerce (at least in AmE) because the noun is too generic. It would be like saying "I like to eat 'food'".
Instead those who work in some kind of commercial business would say, "I am a businessman," although they would be likely to add something specific about what they do, e.g. "I represent a women's shoe manufacturer" or "My company makes medical devices".
"Trade" is a little less clear. If someone said they were "involved in trade" I would assume they have an import/export business. In a different context someone who said they were a "trader" is something like a stockbroker. However, in the UK (and possibly elsewhere), someone who "works in the trades" is a skilled tradesman, like an electrician, plumber, welder, auto mechanic, or many other similar jobs that require some kind of specialized skill set.
To answer your question: Someone who is in business would be most likely to say what they do or what kind of business they are in.
I'm in sales -- for many years I've represented the largest maker of baby cribs in the country.
For many years I've been running a company that produces animal crackers.
and so on.