Connie - TOS canon nomenclature

There's an interesting discussion on similiar (but distinct) ship designs of that nature over on this thread.

 

Related somewhat I suppose:

What defines a "heavy cruiser" in Starfleet? What makes it any different from any other cruiser or starship?

The term itself is a relic from an arms limitation treaty (Washington Treaty) that defines two different classes of cruiser by the size of their gun barrels only. A light cruiser could be much larger than a heavy cruiser (within the tonnage restrictions of the treaty) just it would have up to 155mm guns or smaller. A heavy cruiser was limited up to 210mm guns.

Both were limited by treaty to 10,000 tons. The reason there are even a light cruiser is because the later London Treaty required an even stricter reduction in the number of cruisers with up to 210mm guns so the major powers switched to making around 155mm guns light cruisers that were just as big or bigger than the up to 210mm armed heavy cruisers.

After the war and the last of the heavy and light cruisers were finished, the term started to be used less as countries build guided missile cruisers and then just cruisers instead. And then just no cruisers, since the difference between a cruiser and a destroyer today is minimal.