No. You are simply wrong in this belief.
Commerce is a prerequisite for capitalism, but it is not capitalism.
All Capitalist transactions are commerce, but not all commerce is capitalistic.
Capitalism requires that there is a Capitalist that owns the means of production and uses that ownership to extract all of the surplus value created by the workers for themselves from the transaction. Commerce is an equitable exchange of value between workers and customers.
A person is not a Capitalist unless they extract value from a transaction without providing value additive labour to the process of production.
You can literally not call yourself a 'Capitalist' in a transaction if you are doing the actual labour that produces the added value.
The majority of people that call themselves 'Capitalists' are not actually 'Capitalists', they are a 'Worker' thats lives within capitalism.
Those successful at being a subservient intermediary between the Capitalists and Workers, the 'Managers', are still workers no matter how well that are paid. Their labour to add value to the means of production is being an organizer and buffer between the Workers and the Capitalists so that the Capitalists don't have to do that labour.
Small business owners that still do the work and manage their business are workers until they stop going to work and just extract the surplus value from the business, then they become Capitalists.
A worker that saves up until they have enough savings in whatever form to retire on is still a worker unless they manage to leverage the savings into a form of ownership of a labour additive means of production that they then extract the surplus value from, then they have become a Capitalist.