Both have fairly substantial use (94 and 21 questions respectively). From what I can see, the majority of questions on both tags have to do with reducing, avoiding or minimising waste.
Definitely don't make a tag synonym.
If you take a look at my map of related tags you will see that there are many tags about waste that aren't about waste minimization. At the same time, there is quite a depth of questions that are about minimizing waste.
As a general rule, questions should use the most specific tags available. So if this question is tagged with waste-minimization then it really doesn't need to be tagged with waste. So it might make sense to add more specific tags to some of those questions.
As background reading, I've also written down my thoughts about handling tag trees on Stack Exchange.