Hello Kaoru! I am glad you are following me. There is a difference in meaning between the two uses. In the first case, (I am interested in music), it means that you like music and maybe that you want to learn more about music. ("interested in" implies more than "like") In the second case, I think perhaps you meant "That movie is interesting (to me)" Note that the "to me" is implied, similarly to Japanese. This would mean that you find the movie thought provoking, or enjoyable. I hope it makes sense to you now. Jason

"I'm interested in music" means I like music, I want to learn about it more. Your other example is not correct grammar and actually I don't know what you want to mean.

' interest in'/'interested in' 'interesting' are somewhat different: I have an interest in music (noun phrase) Music is my main interest (noun) I am interested in music (transitive verb, but almost same meaning) Music is interesting to me (adjective) Is this what you were asking? 老鬼

The differences are following: I'm = I am - first person singular pronoun + "to be" in a proper form. It's = It is - third person singular pronoun + "to be" in a proper form. interested - ADJECTIVE describing "I" interesting - ADJECTIVE describing "It" on, in - preposition, usage can be tricky, please check http://www.ego4u.com/en/cram-up/grammar/prepositions for a better idea. music, movie - different objects. "It" is an element in the movie. - you need to give a context for "It" to make it work here, we cannot conclude what it is. Subordinate clause is wrong by itself. So simple.