but does the さん have the same meaning of さま when it means "state"?
You could say so. But its literal meaning is already lost and not felt by native speakers anymore just like any other greeting and overly clichéd old idiom.
If you do analyze the very literal meaning of ご苦労様, it would be
"ご = preffix for politeness,"
"苦労 = noun that means trouble/difficulties/whatever that require a lot of effort," and
"様 = suffix for the sense of 'being in the state of.'"
By explicitly saying these words, you mean, in the most literal sense, "I acknowledge that you have been in the state of having to put a lot of effort."
But, to be honest, it's just a fixed phrase you use when someone has just finished some work. So, asking what 様 means here is like thinking of what "there" means in "Hi, there." You may be able to find an interesting etymology or explanation. But the literal meaning, if ever existed in the past, is already lost. I'm not saying trivia, etymology, and stuff like that are not interesting, though.
In any case, さん here is a much friendlier and less serious version of 様. So, it sounds like the speaker doesn't acknowledge the trouble you've gone through as seriously or appreciate the effort as sincerely as if they used 様. This generally applies to other similar set phrases such as お疲れ様 vs. お疲れさん and お待ち遠様 vs. お待ち遠さん. In all cases, さん is much more informal and less serious.