Lacking an answer for 3 years, I'm going to attempt to answer this based on internet definitions and logic. Please, I welcome any insight from chemistry experts to improve this answer.
First of all, the Wikipedia link quoted actually gives two definitions for protomer. The one quoted is the "structural biology" definition rather than the "chemistry" definition. On the other hand, it seems as though monomer has one definition according to the Monomer Wikipedia article. However, as pointed out by the OP, another point of confusion arises in the definition of a monomer as an oligomer with just one subunit in protein quarternary structure. So we actually have two definitions of each term out there. Let's recap them and then compare.
Protomer (structural biology): In this case, the term protomer is reserved for the specific case of being part of a hetero-oligomer. The "hetero" part is important. The point is that the oligomer is made of a number of different macromolecules- glued together non-covalently. In this case, a protomer is defined as the smallest repeatable unit within this hetero oligomer, which may be the entire oligomer itself (in which case, confusingly, the oligomer is called a monomer). The term protomer in this case, as pointed out by Wikipedia, serves the sole purpose of disambiguation. When we say "blah-mer", as pointed out by Hanry, we are saying "this thing has blah parts". But what are "parts"? Are they quarks? Electrons? Protons? Atoms? Macro molecules? Or... repeatable sub-units. It seems as though the confusion was between the last two. You can break a hetero-oligomer into macromolecules and you'll get a bunch of different macromolecules. You might get 12 As, 12 Bs and 12Cs. So is this a 36-mer or is it a 12-mer? It depends on what you mean by "mer". If each "mer" is an ABC subunit, then it's a 12-mer. If each macromolecule is a subunit, then it's a 36-mer. The term protomer helps us here. The molecule can be viewed as a 12-protomer, meaning that it's 12 copies of the smallest repeatable subunit: ABC.
Protomer (chemistry): In this case, it looks like the term means something quite different. It looks like a protomer is defined as a specific type of tautomer, one in which the tautomerism arises as a result of variable proton position.
Monomer (standard): A monomer is a single molecule that forms part of a polymer. The polymer can either be a homo-polymer, consisting of repeated copies of that monomer, or it can be a copolymer (analogous to a hetero-oligomer), consisting of different monomers, according to Wikipedia's Polymerization article. The key here is that the monomer belongs to a polymer- meaning "many parts". Typically polymers are distinguished by the fact that they can theoretically continue forever in big long chains.
Monomer (oligomer special case): This is just an unfortunate use of terminology, but it kind of makes sense when you think about it. "Oligomer" means "Few parts". Typically the distinction between oligomers and polymers is that polymers can go on forever- they could keep growing through repeated polymerisation, but an oligomer will have a set number of parts, and then it's fully grown. Because oligomers can have a set number of parts, people decided to further sub-classify them by the exact number of parts. So a hexamer is an oligomer with six parts, for example. Following this naming convention, we have pentamer for 5 parts, tetramer for 4 parts... and all the way down to monomer for one part. Which just unfortunately intersects with the other definition of monomer, being a single part of a polymer chain.
So, now that it's been established that there are different definitions even of each term itself, let's try to compare them:
- Protomer (structural biology) vs. monomer (standard): a protomer here is defined as a sub-unit of an oligomer, whereas a monomer is a building block of a polymer.
- Protomer (structural biology) vs. monomer (oligomer special case): in this case, we need to think. A monomeric oligomer is one which has one "sub-unit". If by "sub-unit" what is means is protomer, then in this case the monomer, protomer and oligomer all coincide and are describing the same thing. If, though, "sub-unit" means the smallest sub-molecules that are non-covalently bonded together, then the oligomer is, trivially, a homogeneous oligomer and not a heterogeneous one: it consists of just one molecule so all the molecules are the same. And so, strictly speaking according to the above definition, the term protomer doesn't apply here.
- Protomer (chemistry) vs. Monomer (standard): these two definitions are not mutually exclusive. By describing a compound as a protomer, in this way, we are just saying that there are different tautomeric configurations of this compound out there. On the other hand, a monomer is just something that can form a polymer chain. It's perfectly reasonable to assume that some tautomer could also be capable of undergoing polymerization, and therefore, would be a monomer. I don't know any examples but maybe someone reading can offer them.
- Protomer (chemistry) vs. monomer (special oligomer): The monomer definition here seems to be a bit vague, but in the loosest sense, every single molecule is a monomer. But it seems as though what's meant is that a monomer, in the oligomeric sense, typically doesn't undergo polymerisation with other monomers to form a polymer - it just likes being alone. Still, even with that definition, it's likely that there are examples of things that are protomers, in the chemistry sense i.e. being tautomeric in terms of proton position, and that are also monomers i.e. oligomers that won't bond with each other any further.