Yes, I know they are different. My comment wasn't clear.
I wasn't sure but I've checked it and this happens with WordPress.com blogs, only with blogs that don't have wordpress in the name - but are in fact WordPress.com blogs.
When I press the like button, there's a window asking me to log in. Well, I'm logged in already, but I log in again, the page refreshes, I press the like button again and the same window shows again! Over and over!
The other day I was able to 'like' a post in one of these blogs, but only after posting a comment. On other blogs however I can't like the posts, not even after posting a comment.