Firstly, they both mean "take photos/pictures" in general. You can use them like this:
我们去照相吧。/我们去拍照片吧。 Let's go take pictures.
When you wanna refer to one single picture, you can just add"个/张" in the middle, like
我们在这儿照张/个相吧。/我们在这儿拍张/个照片吧。 Let's take a picture here.
Well, "张"here is just a little bit more formal than "个".When we write about it, we use "张" more often.
Secondly, though you can use them both, now Chinese don't often use 照相 that much as it has somehow become a little old-fashioned, in my very own opinion. It is commonly used in the name of a store(I don't know how you guys call this kind of places where people are taken pictures of and pay for the service and photos) which is "照相馆". You are not likely to hear young people practically say it.
Thirdly, you know, “相” actually means people's faces in Chinese. So 照相 should be used to refer to the action by which we take pictures of other people, not just the scenery. But 拍照片 can be used anywhere.