Equivocation occurs because we attach too much significance to a superficial similarity between words or expressions, viz., that they are spelled the same way. Distinction Without a Difference occurs because we attach too much significance to a superficial difference between words or expressions, viz., that they are spelled differently. Equivocation can occur most easily when a certain word or expression has two or more meanings. If you tell me that you just bought a new house, I will probably ask you whether the house is brand new, or an older home that is just new to you. If you think about your favorite riddles or jokes, you will probably find that some of them are funny because they momentarily confuse two different senses of the same word or expression.
Equivocation is particularly difficult to detect when the meanings of words differ in subtle ways.
We say that a person is discriminating if they are capable of recognizing subtle differences, or if they have particularly good taste. But now suppose I know a woman who can tell just by looking at people from diverse racial backgrounds precisely what their racial ancestry is. I might correctly say that she is extremely adept at racial discrimination. This, of course, would be a very confusing thing to say, and would almost certainly succeed in giving people the wrong idea. To most people this refers to the termination of a pregnancy, but its broader meaning is just the termination of any process whatsoever.