Ronald Coase is famous for a theorem George Stigler invented, which states that all mutually desirable transactions happen if there's no reason for them not to happen. The corollary is that if some mutually desirable transactions don't happen, they don't happen for some reason. This theorem won Coase a Nobel prize. Stigler also won a Nobel prize for different reasons.
The Coase Theorem, named after the person who inspired it, is important because it tells us that the mutually-beneficial-transactions-that-didn't-happen that define externalities would happen if there weren't reasons they didn't happen.
Coase's work is particularly interesting because it suggests that externalities can be understood in terms of transactions that didn't occur. For example, the externalities associated with pollution would be resolved to the benefit of all if certain transactions could be arranged at a sufficiently low cost. Unfortunately there are reasons why that does not happen. But if those reasons could be resolved, everyone would be better off. Say, a technological improvement increasing the supply of markets.
Compare that to, say, the wheat market, often considered about as close an example of a "perfect" market as we're ever going to get. Suppose the market's demand for wheat is such that it demands 50 units of wheat at a price of $5, and it demands 100 units of wheat at a price of $3. The market supplies 50 units of wheat at a price of $5, and it supplies 20 units of wheat at a price of $3. If the market could supply 100 units of wheat at a price of $3 and not lose, that would be a Pareto improvement. Unfortunately there are reasons why that does not happen. But if those reasons could be resolved, everyone would be better off. Say, a technological improvement increasing the supply of wheat.
So I propose the Stigler theorem: some potentially Pareto-improving transactions of wheat do not happen because the cost of wheat is not zero.
I propose a more general theorem: some potentially Pareto-improving transactions of anything do not happen because the cost of something is not zero. There are an infinite number of theorems that fall under this general theorem, all of which are presumably worthy of a Nobel.
None of these theorems fall under the Coase theorem. Transaction costs are distinct from wheat costs, without affecting the welfare analysis in principle. Rather, the Coase theorem falls under this more general theorem.