A symlink (though some filesystems handle symlinks differently) is an inode table entry that points to the same place as another file (or directory).
For example if foo is inode 1234 then bar (a symlink to foo) is inode 1234.
bar doesn't really exist it's just a pointer to a "real" file.
Symlinks generally don't have permissions outside the permissions of the file they point to. So bar's permissions are "the same" as foo's. You can't set permissions on bar (the symlink) only on foo (the real file).
That being said, it's a really high level view. Different file systems handle symlinks differently. Different tools handle symlinks differently. Some file systems "flag" symlinks and handle them specially, but some don't.
For example chmod on Linux won't change a symlinks permissions but on OSX you can get it to. In both cases the real files permissions are changed.
I can not think of any system (doesn't mean it's not out there) where a symlink has permissions separate from the real file.
chmodsets permission bits (rwx and sticky/setuid/setgid bits, ...) : this is what we call a "mode". But you seem to be referring to file types instead.