The terms "profession" and "business" are different faces of many enterprises; and to some people there is little difference. But those who see their enterprise as related to one, or the other, tend to naturally focus on the one, or the other, face.
The two concepts have developed over the centuries. Long ago there was no money; there was only subsistence living. One did not "make" or "earn" "a living"; one foraged and gathered it, or hunted it, or with the development of agriculture, cultivated it.
Then "exchange" naturally occurred; you give me some of the excess which you grew in exchange for some of the excess that I caught. Then "looking for a better exchange" naturally occurred; and a medium of exchange, money, developed.
Then "occupation", making a living, became relevant. Then specialization and the concept of having a "trade" was invented; historically a trade indicates an occupation involving manual training and skill. And then the concept of "craft" developed; in the occupational context first, and in "arts and crafts" later. One with a craft (a craftsman) is assumed to have more specialized skill than one with merely a trade.
And other concepts evolved including "artisan" and "artist".
Then "profession" was distinguished from the other concepts; the term profession indicates more intellectual than physical; knowledge and mental-intellectual skill more than manual-physical skill; working with ideas more than working with things.
In previous times an occupation itself was distinguished as a trade, a craft, an art, a profession.
But today the distinction is also influenced by how one approaches the occupation; the craft focuses on the doing of the job, the profession focuses on the ideas and the intellectual faces of it. Any occupation today can be embraced as a trade, a craft, an art, a profession; they each have different perspectives.