They are not the same thing today.
I concede that conservatives may be (by and large) - registered republicans. The republican party may have traditionally been the only viable antithesis available as a counter to democrat tyranny, but it certainly doesn't mean all republicans are conservative. In fact, too few are. The big problem with republicans today is that the establishment has openly and willingly distanced itself from conservative, traditional values. No one knows what the GOP stands for anymore, except appeasement, since it's leadership stopped fighting for its soul and just surrendered it to the left.
Both parties are far more conservative than they were in the past. They might be slightly less religious and less discriminatory towards minorities in the past (which is a good thing, though I'm barely seeing that with many of today's republicans), but in all other aspects they are more conservative than even 20 years ago. If you really think they're too liberal, it seems like they've also got a very effective reality distortion field.
I'm all for fiscal conservatism, but today's conservatives (who I maintain primarily associate themselves with the GOP) are too backwards on everything else. I cannot support a party that practically institutionalizes discrimination.