Question: both on this forum and in my office people are using the word "puente" when a holiday falls on a Friday or Monday making a three, or in some cases four, day weekend. Other places I've lived, a puente was when the holiday fell on Tuesday or Thursday and people extended it by taking the intervening Monday or Friday off making a four-day weekend. Is it just an evolving term, or is that how it's always been used in Spain?

Your guesses are pretty much on the mark. As far as I know, a "puente" is technically a day off that you take to join the weekend with a holiday, but nowadays a lot of people in Spain use the term for any old long weekend, even if the holiday falls on a Friday or Monday.

puente is like a bridge its an extention of a legal holiday in order to extend it. it does not matter where it falls as long as it is used for the extension of that.. holiday.

Actually I think the word "puente" really alludes to the fact that you bridge the holiday with the weekend. At least it makes sense when used that way. In fact, people will ask in those situations whether or not you are going to "hacer puente". So, there are times when people differentiate between a "puente" and having a weekend and then, say, a holiday on Tuesday.
That's especially true of moments like "puente de diciembre", when Dec. 6th and 8th are holidays and all sorts of crazy combinations come up, especially when they fall in the middle of the week, like last year.

Puentes can be official, that is, everyone gets the day off, or individual.

Still as I said before, regular long weekends are also called puentes.