Evidence in favour: The sun is a light source, they are much dimmer light sources with much smaller radii, consistent with the hypothesis.
Evidence against: There are none at intermediate distance, they're either the sun or so far away to practically be a point light [1]. The sun is yellow, they are not [2]. The sun has a partner in size (measured in portion of the sky it takes up) with the moon, which I presumably know is relatively close by, suggesting some form of relation between them [3].
Ultimately I know that there are lots of ways to give off light. Fire, fireflys, lightning, the sun (if it isn't fire), hot metal, sparks from static electricity, ... There just isn't enough evidence to believe that it's more likely that the stars are the same source as the sun than yet another source.
[1] As it turns out "so far away to be a point light" is the intermediate distance, but that result requires an amount of empty space that I would find unlikely. I haven't checked this but I suspect a statistical analysis would also find it unlikely. Assuming all stars are the same size as our sun, and that they're distributed uniformly in space. Given that I count the stars and come up with a reasonable minimum and maximum distance bound from their brightness, I suspect it is extremely unlikely that there are as many as there are but none close enough to be noticeably brighter. This result (assuming it is true) is of course the result of the fact that many stars are far larger/brighter than the sun, so we're actually sampling from a much larger volume than my naive estimate suggests.
[2] I'm not sure I fully understand this one... the sun appears yellow because of some quirk to do with the light the atmosphere lets in, but why doesn't that make the other stars yellow too?
[3] Pure coincidence