If your spouse asks you whether you remembered to mail the tax forms and you say “Yes,” even though you know they're still sitting on the passenger seat of your car, you're telling a lie, which is a deliberately false statement. If you launch into a lengthy explanation of the day's frustrations and setbacks, the correct word would be prevaricate, which is to quibble, dodge the point, or confuse the issue so as to avoid telling the truth. If you tell your spouse that you would have mailed the taxes, but then you started thinking about an important deduction you might be entitled to take and decided it would be unwise to mail them without looking into it, you're rationalizing, which is to come up with reasons that put your own behavior in the most favorable possible light. If you say that there was an accident in front of the post office that prevented you from finding a parking space and there really wasn't, fabricate is the correct verb, meaning that you've invented a false story or excuse without the harsh connotations of lie. Equivocate implies saying one thing and meaning another; it usually suggests the use of words that have more than one meaning, or whose ambiguity may be misleading. For example, if your spouse says, “Did you take care of the taxes today?” you might equivocate by saying “Yes,” you took care of them—meaning that you finished completing the forms and sealing them in the envelope, but that you didn't actually get them to the post office.
