I know most of the danish-norwegian navy, but I assume that other navies of the time had similar practices
While there are exceptions, generally it holds true (mid 17th-late 19th cent) that a frigate was a ship with an unbroken battery deck (most often covered, but not necessarely). Further more the ship had a full "sail plan" (Not sure of the correct word, maybe full rigging?) on 3 masts.
F.ex. this
http://www.hardysweb.dk/images/JYLLAND.jpg
is a frigate (Jylland 1860). With a full sail plan on 3 masts and an unbroken (covered in this case) battery deck (It also had guns on the deck, but that's not important). Notice that this is a "screw-frigate"(Correct word?) who also had a steam engine propulsion.)
this ship Najaden (approx 1800)
http://www.orlogsbasen.dk/tegn/91-2000.jpg
This ship is also a frigate due to 3 masts with full sail plan and one unbroken battery deck. Note that the battery deck is not covered.
This 1664 ship
http://www.orlogsbasen.dk/thumb/A931.jpg
and this 1687 ship (Elefanten)
http://www.orlogsbasen.dk/mthumb/187-2000.jpg
(The model is, btw, an orginal model)
Strictly speaking we don't know the sail plan of those two, assuming something like a full sail plan, they are also frigates.
If we go much further back than mid-17th century, at least in the danish navy, the term "frigate" seems to simply have been used to denote a warship of significant size, and seems to have been used interchangeably with the dutch word "Orlog" (ship) which means a War(Ship).
Another problem of early 17th century ships is that the details of the rigging of the ships are often unclear, and it's a point of discussion when "full sail" plans becomes a standard.
Frigates and lineships had full sailplan, and respectively one or more than one unbroken battery decks. That was the main warships. Now a ship that wasnt a frigate (because of a broken battery deck) but had a full sail plan was, at least from around 1800s) known as a "brig" or "Orlogsbrig" (War-brig). Irrespectable of the ships that had a brig rigging (a two mast ship).
Ships of the navy that weren't with a full sail plan and weren't brigs was simply known as a "Skonnert" (maybe the same as a Schooner?). Eventhough a skonnert, is also a ship with specific sail plans, but in the navy it had a different meaning.
The danish navy use of "Skonnert" are alike, I assume, to the RN use of the word "Bark" (not to be confused with a barque)
Large warships usually had full sail plan, since that was the best sail plan for a given mast in terms of wind force. But it required a lot of hands, something that warships anyway had. Merchant ships rarely, if ever, had a full sail plan, and used other, less manpower hungry, rigging.