I have looked these two words up on WWWJDIC and there doesn't seem to be much difference. Are they interchangeable, or do they infer different things?
出かける is a compound verb made from 出る and かける. In that sense, it is natural that the meaning is similar. But, they are different.
出る has several meanings, but the most general idea is 'something moves out of a certain range.'
出かける is something like 'going out,' but only used when "A human being goes out for some distance by his/her own will." Something closer to 'to travel.'
According to a paper, "複合動詞「〜かかる」と「〜かける」", this 「かける」 is classified as 志向移動, intentional movement. That means, 「出かける」 requires some intention or purpose toward destination or movement. http://repository.tufs.ac.jp/bitstream/10108/20525/1/jls006003.pdf
Maybe these two examples explain the difference well.
- 火事になったので、外へ出た。(Because of the fire, I got out.) (There is a certain range. Probably a house in this case, and I am now out of it.)
- ゲームに飽きたので、外へ出かけた。(Because I got tired of playing a game, I went out.) (I am looking for some fun, and I move for a while.)
You cannot say,
- *犬が出かける。 (A dog cannot have a complex intention.)
- *表へ出かける。 (表 means 'in front of the house.' That is too close, too short a distance.)
- *手錠をかけられて警察へ出かける。 (You are dragged by the police, not by your will.)
- *火事になったので、外へ出かけた。(If it is on fire, your intention is to avoid the fire, not to go to the destination.)
are all natural.
I also see a difference in the に-object. 「〜に」of 出かけた is a final destination or intention. On the other hand, 「〜に」of 出た is the place you just reach after the movement.
- コンサートに出た。(You appeared on the stage.)
- 旅に出かけた。(This has an emphasis on the fact that you are traveling.)
- 旅に出た。(This has an emphasis on the fact that you are absent.)
The difference between the last two would be interesting.
「旅に出ます。探さないでください。」is a common expression in a letter for running away from home. (Well, at least in fictions.)
This is not「旅に出かけます。探さないでください。」. This makes me feel safe because s/he has some objectives while traveling, and s/he would be back after s/he finishes his/her quest.
出る is much more universal. It has a VAST pool of different meanings and can be used very loosely compared to 出かける which has a very specific meaning
出かける usually means 'to leave for some sort of business', where the 'business' can be as mundane as a walk. You are generally expected to get back.
出る is a more universal 'to leave' or 'to exit'