Comment by morpheuskafka

A TN visa is a visa, but what someone is “on” is a status, not a visa. Visas are only relevant to the moment of entry. You need a visa of type X to ask to enter with status X.

The exception to that is Canadians like OP, they don’t need most visa types (the E investor/trader visa is the exception—but TN, H1B, etc., don’t need).