Type III cement is a form of portland cement. This article explains Type III cement, but basically, Type III is a high-early-strength cement. It is ground finer and reacts faster than Type I cement, so the early strength gains are greater. Note the word “early”.
Generally Type I cement based concrete reaches about 60% of its 28 day strength in the first 3 days;
Type III cement achieves about 70% of its 28 day strength after 3 days. That is indeed a little faster than Type I.
With either Type I or Type III portland cement, continued strength gain requires continuous wet curing for weeks. Concrete that dries out prematurely never reaches its full potential. (Note however that with concrete countertop mixes that achieve over 8000 PSI compressive strength well before 28 days, it is really not necessary for them to reach their full potential. They are strong enough after a few days, so I generally cure regular portland cement mixes for only 3 days.)
CSA cement typically achieves 80% or more of its 28 day strength in the first 24 hours, and usually close to 100% of its strength within the first 3-7 days. Because of the very rapid reaction, wet curing is necessary only for the first few hours, not continuously for weeks like with Portland cement based concrete.
In the graph below, note the steeper curve for Type III, meaning faster strength gain.
Strengths of type I vs type III cement
Figures taken from PCA, Design and Control of Concrete Mixtures, 2003.