On concept albums there can be a whole story told through music and theres a lot more depth and meaning to the album than on a regular album. A great example would be the new Moonsorrow album, theres the post apocalyptic theme on it and the music tries to really create that feeling and atmosphere. Theres a whole story on the album too that tells about a group of survivors that have to move out of their town because it was inhabitable. Each song tells some part of the story and has also other meanings, like Muinaiset tells about how the group who survived the apocalypse is trying to settle in the woods, and it also tells about the ancient powers of nature and how they're taking over the world after humanitys gone. A regular album is just filled with songs that arent connected in any way. They dont tell a story or have a bigger meaning as a whole.
I agree though that there isnt a lot of difference on a more loose concept album (Which maybe just has a certain theme and doesnt tell a story or anything) and a regular album.