They are, indeed, the Sun and the Moon.
The Moon does in fact shine light on the Earth. That this light is ultimately reflected from the Sun does not disqualify it; it is still causing light to reach the Earth. That the Sun is, scientifically speaking, a star, does not disqualify it.
Similarly, other planets (and distant galaxies) would be called "stars" for quite some time, and indeed, still are in colloquial use.
You are overthinking this. "Stars", here, are merely light sources (again, not necessarily producing their own light) which are much smaller/weaker, as seen from Earth, than the Moon. The separation between Sun/Moon and stars is one of function, not of substance. That this is the correct distinction is plainly evident in context, as the "stars" are "for signs and seasons" ("signs", in particular, suggests the inclusion of other Solar planets), and the "two great lights" are for illuminating the Earth.
What is incorrect is ascribing a mutually exclusive, one-to-one correspondence to "stars" as used in this functional context and what an astronomer would call a "star".
You also said:
If the Bible say "two great lights" then both of them are lights,
NOT one of them is not light but reflect something else's light.
...but again, I think you are trying to be overly pedantic while reading a text that is meant to speak more to effects than pedantic scientific reality.
For that matter, consider a fluorescent light bulb. Would you call this a "light"? Would you say it emits "white" (whitish, anyway) light? Would it surprise you to learn that a fluorescent light bulb is actually an ultraviolet light, and its "useful" light is actually secondary emissions from the phosphor coating? (Some white LEDs work similarly.)
Now, if a fluorescent light bulb does not directly produce visible light, but it still called a "light", why can't other indirect illumination devices also be called "lights"?
I suppose if you wish to pursue that further, you could ask on Hermeneutics whether the Hebrew word used can legitimately refer to an indirect light source. AFAIK, however, most people understand the second of the "great lights" to be the Moon. However, I would note that the initial "light" has an indeterminate source and thus is perhaps meant to refer to the actual photons providing illumination. In this sense, "the Moon" certainly qualifies; or, to be more pedantic, there are two "sets" of photon streams, both of which are originally produced by the Sun, but which are perceived on Earth as "the Sun" and "the Moon".