Forget the vague speculations about marginal differences in displacement, speed and armament. The real explanation of the difference can only be found in naval history. It amazes me that so few people, otherwise very knowledgeable about modern warships, know how the modern frigatedesignation came to be. Most will give you vague generalizations, which won't leave you any wiser, probably more confused.
Watch this video and you'll find out that there is no definite yardstick which will conclusively determine whether a warship is either one or the other. That saves a lot of pointless speculation. It's just a matter of preference and naval culture.