Hoarding is when you can't let go of almost everything, you have an emotional bond or attachment to it. So it gathers up in your home, amongst other things. It's like an addiction, you can't get rid of things. Once they start piling, it becomes harder and harder to clear out. It's unhealthy.
Collecting is if you're intrigued by a certain topic, and you either seek out objects relating the topic, or come across them by chance. Those are the best, in my opinion, because it's one specific item you keep finding, it symbolizes something.
Both are different, but both involve finding, and holding onto stuff. Either way, people have a bond to things, and that's what pushes them to seek these things out