Comment by rhines
When I looked at working in America several years ago, many people I spoke to and people commenting about it on Reddit/HN/Blind emphasized that it's TN status, not TN visa. They even suggested that calling it a visa when trying to enter the US could get your application rejected. I'm not sure if things have changed since then but if so there's probably lots of people who heard that same advice in the past and haven't learned the updated info.
Visa and status are different things and exist simultaneously. A visa is used to cross the border, a status is what enables one to be in the country. Many people on H1B don't have a physical H1B visa either as they have "adjusted status" from some other status to H1B without leaving the country and hence cannot possibly have a visa, which can only be issued in a US consulate, which don't exist in the US per se.
Colloquially people refer to a status granted through a particular visa category as "visa" e.g. "I am studying on F-1 visa", "H-1B visa employees" etc.