I found in Manga Updates that there are Web Novel and Light Novel versions of Re:Zero.
So are there any differences in them, like plot, characters etc.?
In any adaptation of a story from one version to another, there are going to be some edits. Originally, Re:Zero is a web novel and it is always the furthest along in the story. The story gets edited a bit as it gets transferred to the "official" light novel publication, and even more as it gets drawn as a manga.
As far as my experiences though, the overall story does not really change between these mediums. It seems mostly just a case of how much content makes it through to each. This is, of course, the most visible between the manga and anime adaptations, since the studio is limited to certain time constraints.
From what I've heard from the community regarding Re:Zero, the light novel is what is considered the most canon/official.