What is the difference between a Conservative and Republican?

Answer 1

In theory, because they are bothe the main right-wing party in their country the answer is yes.  However, in practice their policies are very different.  Britain in general is a lot further left- wing meaning that the conservatives are more like the democrats than the republicans. 

Answer 2

It's a matter of loyalty. A Republican has his primary loyalty to the Republican Party.

A Conservative has his primary loyalty to the Constitution of the United States.

There are a great number of Republicans who aren't especially concerned with the Constitution.

Answer 3

The Republican party is a party of conservative ideals, just as the Democratic party is a party of liberal ideals.

Many people have conservative ideals and therefor are 'conservatives' but, do not believe in organised politics or generally do not agree with the Republican party's actions so do not identify as Republicans.