[daotoad]

My understanding is that a star is a star regardless of what is or isn't in orbit.

A sun, however, needs to have planets to be a sun.

[rzzzt]

I searched if there are "free-floating" stars that don't have any planets in their field of gravity, and results essentially say "not since the early days of the galaxy". So nowadays all/most/the overwhelming majority of stars are suns. Very interesting!