"He is afraid of swimming."
Translation:Él tiene miedo de nadar.
The page you list (as well as the others I've read) contradict DuoLingo's word choice. "Miedo" is supposed to be a fear of something very real and present, like "that dog", "those bears", etc. Basically, if you can point to it, it would be "miedo". "Temor", on the other hand, seems to be a general dread or phobia... of situations, like "flying", "swimming", or maybe even "dogs" as opposed to "that dog".
Chogas: by now you may already know that in Spanish we can not use the present participle and turn it into a noun/gerrund, as we do in English. The infinitive 'nadar' (to swim) used as a noun is used the same way as we use the gerund. Spanish grammar does not provide for a gerund (Swimming). Edit to say: your question is a valid one. We are all trying to learn here.
I tried several other verbs in google translate with the sentence and they all followed the pattern "He is afraid to" only "nadar" lead to the same construction as duolingo. Well I correct that "caminar" behaves like "nadar" I guess "He is afraid to swim" is probably a valid translation too.
From my understanding, there are certain situations where one is preferred over the other, but in general I believe that the two expressions are interchangeable. It's possible that "tender miedo de" is used more often when a verb is involved, but from my understanding you can use "a" as well, report it. http://forum.wordreference.com/showthread.php?t=248029=1530873#post1530873