Felicia ... I can't give you any real insight on which specific pain meds do what, but there is a difference among them as to what kind of pain they relieve.
My husband has had chronic back pain for 20 years, and the doctors (when they bothered to listen ... some great ones did) generally just kept upping the dosages. We recently acquired an insurance case worker (she had been an oncology nurse), and she reviewed his med list and said, "Why is there nothing here for nerve pain?" ... since nerve pain is what he has. Also, his pain meds had terrible side effects from nausea, etc., and he has struggled against continual weight loss. She made a list of suggestions for his pain clinic, and of the several possibilites he tried, he found out what works. He now takes one general pain pill and one for nerve pain. And the nausea is pretty much gone.
On the pain scale, he has gone from an 8 or 9 (out of 10 maximum pain) to a 3 or 4.
SO ... yes, pain meds do affect different types/causes of pain, and sometimes it takes a while to get the right combination or dosage to achieve optimum effect. If your husband's current medication isn't doing the job, talk to the doctor. There are meds out there that probably will help, and your doctor should be compassionate and professional enough to help you figure out what is best for your husband.
Good luck.