A hobby is what we do in our leisure or spare or free time. Something we do with devotion. Like Stamp collection.
Interest is the feeling of a person whose attention, concern or curiosity is particularly engaged on something. For example He has a interest for singing.
Hobbies are the things you would like to do in your leisure times......but your interest is the one which makes you find time for doing so....for example if you have interest in art will surely have some time to execute your interest...but if art is your hobby you'll just do it whenever possible...