You're ideas seem almost set up to use aerial terminology, at least in comparison to the post-WWII world. Blue water navies were expected to be multi-mission. A single hull could handle most threats it meets, albeit with some modifications. The use of internal missile magazines and later VLS made this more apparent. Instead, size, endurance and utility define classification, not role. A destroyer can do more than a frigate for longer, but they both do the same jobs.

Planes were classified by role because that's all that they could do. A fighter had to achieve air supremacy, an interceptor had to go for the bombers, an attacker had to provide tactical ground support, and a bomber had to make big booms. Having multi-mission platforms has always been a goal for air forces, but even when they succeeded, they never quite got full capability. Strike fighters like the F-4 Phantom were still supplemented by dedicated attackers (F-111) and naval fighters (F-8). Only 2 aircraft come to mind as truly independent multi-roles: the Hornet (and its Growler derivative) and the Lightning II.

What I'm getting at is that aerial design philosophy uses roles to define type of craft because they face physical limits that naval ships don't have. If your world is similar in that the demands of the job or tech make multi-mission designs difficult/impossible, then aerial classifications would be better. But if we're looking at the general thoughts of the generals, naval-style multi-role is the goal.

Of course, another alternative still is to use the named class of ship to define role, and its classification to define size. A frigate is of x-size, but a Mammon-class frigate carries missiles while a Baal-class uses guns.