Republican and Liberal?

I had a question about these two branches, Why are the main types of people that vote catagorized as one of these? Now can I ask, if someone is truley one of these wouldn't it be beneficial for that person to completely, in whole, (without any 'well what if' s) back the person they vote for? I swear if anyone answers...well I did, your comment will be removed, unless explained. What I'm saying and asking is, For someone to call themselves republican or liberal would they not have to be completely in accord with the person they elect? If you truly, after reading what the president you selected to become, agreed wholeheartedly with every statement that he issued, does that not make you somewhat naive and maybe foolish? So why call yourself something, that if you have any sort of somewhat intelligent brain, you would realize would be a mental and physical impossibility because no one is in exact accord with anyone else, am I correct?