When it comes to navys, there are basically three types of navys.
Brownwater navy: Coastal defense forces with no oversea capabilitys, mostly patrol boats and corvettes. Doesn't mean primitive navy, for example the Swedish anvy is a Brownwater navy.
Greenwater navy: Navys with limited oversea capabilities, mostly in the seas and oceans the border. Often well equipped and sized, but simply lack the bases and ships for world wide action.
Italian, Spanish, Brazilian, Japanese,German/Dutch Navy are good examples. Often have either alrge amphibic attack ships or small carriers.
Bluewater Navy: World wide active navys, best tech and ability to send forces nearly everywhere. Carriers are a must, just like a large support fleet.
US Navy is the best example, but also French, British, Russian and maybe even the chinese Navy.
Ships:
Can be divided in 4 types:
Light ships: All kind of boat (Patrol, Attack, Missile) and Corvettes. Small ships with limited range and armament, often used as escort and Patrol. Anything below 2000 tonnes normally.
Heavy ships: Frigates, Destroyers, Cruiser, Battlecruiser (Mother Russia ). Major war ships with strong armament and large range. These ships can either be used on their own, for pwoer demonstration or in Task forces and battlegroups, grouped around the support and transport ships.
Capital ships are mostly Carriers these days. Carriers can range from very small ones with hardly over 10 000 tonnes (see thai navy), Helicopter Carriers like the Mistral-Class or the Japanese navys ships, to small carriers (see Italian Cavour), Medium Carrier (Russian Kiev-class, French Charles de Gaulle), Large Carriers (British Quenn-Elizabeth-class) and of course Super Carriers (See Us-Navy).
Lastly Submarines. Two kinds of subs. Attack subs, small subs armed with torpedos mostly meant to attack cargo ships aor infiltrate enemy tasks forces for carrier sniping (German Fuel-Cell are currently the best at this). And Second, of course strategic Subs, with Nuclear missles, lots of them.