In a relational database all types of relationships are represented in the same way: as relations. The candidate key(s) of each relation (and possibly other constraints as well) determine what kind of relationship is being represented. 1:n and m:n are two kinds of binary relationship:
C {Employee*,Company}
B {Book*,Author*}
In each case * designates the key attribute(s). {Book,Author} is a compound key.
C is a relation where each employee works for only one company but each company may have many employees (1:n): B is a relation where a book can have many authors and an author may write many books (m:n):
Notice that the key constraints ensure that each employee can only be associated with one company whereas any combination of books and authors is permitted.
Other kinds of relationship are possible as well: n-ary (having more than two components); fixed cardinality (m:n where m and n are fixed constants or ranges); directional; and so on. William Kent in his book "Data and Reality" identifies at least 432 kinds - and that's just for binary relationships. In practice, the binary relationships 1:n and m:n are very common and are usually singled out as specially important in designing and understanding data models.