I hate things that make me angry. I abhor things that make me feel disgust. That having been said, we often use "hate" to mean that we really think that something is bad, so the two words can be very similar. I rarely use the word "abhor". I might use the word "loathe" instead to mean that I really do not like something.

Abhor is stronger, but the meaning is the same. http://learnersdictionary.com/definition/hate 1 : to dislike (someone) very strongly : to feel hate for (someone) [+ object] He was a cruel tyrant who was hated and feared by his people. She hated them for betraying her. They were political rivals who truly/bitterly hated each other. [+] more examples [no object] children whose families have taught them to hate — opposite love 2 [+ object] : to dislike (something) very strongly : to find (something) very unpleasant She hates [=really dislikes] cold weather. I hate spinach. I hate doing this. http://learnersdictionary.com/definition/abhor : to dislike (someone or something) very much They abhor [=hate, loathe] violence/racism. She simply abhors [=despises] exercise and hates to diet.

Sometimes we want to use a verb which signifies a stronger than usual emotion. Therefore we substitute love for adore and hate for verbs like abhor, loathe or detest.