Monomers
Monomers are identical or strongly similar molecules that can be joined together to make biopolymers.
Biopolymers
Biopolymers are threads of repeating units, (amino acids are the repeating units in proteins), that can be later twisted into shapes. The threads have an advantage: they are easier to shape into specific formations. Which is easier, after all, to shape into an art form, -- wire or marble?
A side note: In praise of regularity
Regularity is almost always preferred in a biological structure. Why? It is much easier to code the DNA for a linear structure with repeating units than for a more complex pattern. All the code has to spell out is which elements and in what sequence.