Hi there, maybe I can answer as to those specific terms and then give you some links to previous answers about classes of ships (and other vessels), and see if you have some questions. Hope that works!

The first thing to get out of the way is that "ship" has a specific meaning during this time. A ship was a large sailing vessel with at least three masts that was "ship-rigged," that is, carrying square sails on the foremast and mainmast with a lateen or gaff-rigged spanker on the mizen. A "man of war" is a square-rigged ship designed to be fought in battle, distinct from a merchant or transport ship which might also be square-rigged but not meant for fighting. A frigate is a small man-of-war, meant for convoy duty or scouting but too small to lie in the line of battle. Line-of-battle ships, or "battleships" as they were later called, were large ships with two or three or more gundecks that would traditionally form a line astern and batter an enemy line. A dinghy is a small boat, like a ship's tender; a schooner is a small vessel not ship-rigged. There are myriad other classes of small ships, like sloops, brigs, barquentines, corvettes, settees, polacres, xebecs -- the list goes on.

During the time you're referring to -- let's bound it roughly say 1700-1815 or so, given "pirates" and "Master and Commander" -- the British navy recognized ships as being in six "rates." From small to large those would be:

• Unrated ships (sloops, brigs, cutters, schooners): 1 gun deck, < 20 long guns
• Sixth-rates (frigates): 1 gun deck, 24-28 long guns
• Fifth-rates (frigates): 1 or 1.5 gun decks, 32-44 long guns
• Fourth-rates: 2 gun decks, 50-60 guns (declining rapidly towards 1800)
• Third-rates (line-of-battle ships): 2 gun decks, 64-80 guns
• Second-rates (line-of-battle ships): 3 gun decks, 90-98 guns
• First-rates (line-of-battle ships): 3 gun decks, > 100 guns

HMS Victory is a first-rate ship.

(The list above is borrowed from a previous answer, btw.)

Regarding more specifics on this, you can check out these answers:

##Overall ship design:

https://www.reddit.com/r/AskHistorians/comments/44sivx/ship_design_and_construction_in_the_age_of_sail/

https://www.reddit.com/r/AskHistorians/comments/20x9kz/classes_of_vessels_during_the_age_of_sail/

https://www.reddit.com/r/AskHistorians/comments/3pn7v5/what_changes_occurred_in_the_construction/

##Frigates:

https://www.reddit.com/r/AskHistorians/comments/2fs8qr/how_much_more_advanced_was_a_british/

https://www.reddit.com/r/AskHistorians/comments/2709jm/how_would_a_britishhms_frigate_built_in_1715/

##General

https://www.reddit.com/r/AskHistorians/comments/25nush/how_common_was_it_for_the_royal_navy_to_send/chjilgb

https://www.reddit.com/r/AskHistorians/comments/2n5n5k/in_age_of_sails_how_various_navies_determine_the/

Paging u/jschooltiger, who probably knows things about these things.

(Is this even allowed as a top-level response? Not sure.)