They're very similar, just a slight shade of difference in meaning.
Intrigued has a little more of a sense of "mystery" and of the unknown about it, than just plain interest.
You can be "interested" in something that you already know a lot about. for instance, I'm "interested" in dogs, or in computers, or in music, etc. It can ALSO be used about things you don't know about yet but want to know more about, just like "intrigued".
You generally are "intrigued" by something that you don't know about. A story, an old building, a set of "clues" regarding a mystery. Once you know and understand something you generally aren't "intrigued" by it anymore.
A last note... we can say I'm interested IN something, but never that i'm interested BY something.
It's exactly the opposed with intrigued... we can say we are intrigued BY something... but not intrigued IN something.
but we can say with both: "blah blah thing/story/person/whatever [interests / intrigues] me"
Hope that helps!