What is there difference between these two expressions, or are they synonmyous?
There are, in fact, two different words written 别人.
The first is pronounced "biérén" and is a noun. It means "other person (other people)" (另外的人). An example of its use is a sentence like
屋子里只有我和他，没有别人。 Only he and I are in the room, no one else.
The second is pronounced "biéren" (note the neutral tone on the second syllable) and is a personal pronoun. It is used to refer to people other than oneself or the person in question. Dan provides a good example (though I would have used 扔 instead of 丢 -- a native speaker will have to weigh in here); in "是别人丢的", 别人 is a pronoun.
As far as I know, 别的人 can be used in place of 别人 in both cases. Nevertheless, I think 别人 is more common in general, and for some reason I tend to think that 别的人 is more naturally a noun than it is a pronoun.