For the purposes of thinking about language, it is helpful to distinguish between three sorts of comparison: literal comparison, imaginative comparison, and analogy. (There are also degrees of comparison in grammar, that is, formations like "big, bigger, biggest".)
Literal comparisons, in which one thing is said to be similar to another in a certain respect, are the simplest. We may use comparisons of this sort to describe or explain things. "A bus," a mother might say to her child, "is like a car, only bigger." A teenager might have to tell a grandparent that an i-pod is like a record-player, only smaller. An old-fashioned history teacher said that he couldn't see the sense in fixing a typewriter to a television screen -- he thought that the first computer he had seen was like that.
Somewhere between literal comparison and imaginative comparison comes analogy. An analogy is a comparison that, without being creatively figurative, tries to explain or describe one thing in terms of another. The clearest examples of analogy have the form:A is to B as C is to D, i.e., the relation of A to B is similar to that of C to D. Thus to explain how recent, in the context of 'archaeological time', is the appearance of human beings on earth, we might draw an analogy between the whole of the earth's lifetime and an ordinary day and say that the first humans appeared well after 11 o'clock at night, and written history occupies only a minute (i.e., the relation of human life on earth to the earth's entire lifetime is like that of the final minute of a day to the entire day). The adjective from analogy is analogous. (The 'g' in analogy is 'soft', like the sound at the end of "fridge": IPA: /ən ˈæl ədʒ ɪ/. The 'g' in analogous is 'hard', like the 'g' in "get": IPA: /ən ˈæl əg əs/.)