In modern analytic philosophy there are several debates about the fundamental nature of properties. These center around questions such as: Are properties universals or particulars? Are properties real? Are they categorical or dispositional? Are properties physical or mental?
The anti-realist position, often referred to as nominalism claims that properties are names we attach to particulars. The properties themselves have no existence.
Relations are true of several particulars, or shared amongst them. Thus the relation "... is taller than ..." holds "between" two individuals, who would occupy the two ellipses ('...'). Relations can be expressed by N-place predicates, where N is greater than 1.