they technically have different meanings. and these two verbs can be distinct from each other. for example, 決まる is intransitive verb. and 決める is transitive verb. While English transitive verb requires object word as you know, Japanese transitive verb likewise needs object word following itself. I'll put the examples with the sentences Chi/小千 san showed. 決まる：日本へ行くことが決まった it literally means "Going to Japan was decided". (weird English though...) 決める：日本へ行くことに決めた literally means "I decided to go to Japan". whereas 決まる doesn't need object word, you have to put object word following 決まる. I hope you could make sense out of these verbs and sentences.

決まる: dicided, things were done. 日本へ行くことが決まった。: It was dicided to go to Japan. 決める: dicide something. 日本へ行くことに決めた。: you have diceded to go to Japan. I'm not sure English translations are correct. If they are not enough to understand, ask me again. or you will probaly have better answers here ;)