So, here's the entry on the 'Sailing Ship' on d20pfsrd. As you can see, the Ultimate Combat version says that it's 20ft by 75ft. Furthermore, it can carry up to 20 large siege engines in banks of 10. I didn't know ships were actually colossal-sized bags of holding, because this is what that looks like. There's no space for literally anything else.
The Skulls and Shackles description of 30ft by 90ft is a little better, until you remember that a Sailing ship can also fit two large sized siege engines on both the front and the back of the ship... and that each of those cannons requires a minimum of two crew members to operate. This is an incredibly cramped ship!
Things get a little better if you assume that cannons are 5x10 objects, and you sorta hang them off the side of the boat... and you increase the size. At least you can add some stairs and masts! For reference, the 2x2 squares are Ballista. I couldn't reason that those are anything less than 10x10.
Is there something I'm missing? Is the 20x60 size the 'free' deck? Is the ship weaponry assumed to be part of the ship itself and the whole of the 20x60 deckspace is for people?
Cannons could be and were squashed into smaller spaces than that. The sailing ship is based on real world sailing ships, not the size they'd need to be with 5'x10' cannon.
Most cannons likely aren't more than 5 feet wide, so would actually occupy half the space of a Large creature. And people standing shoulder to shoulder (like in formation) would occupy the same square as other people. A 3 foot tall halfling and a 7 foot tall orc both occupy the exact same amount of space, as far as the combat grid is concerned (and have the exact same reach with a weapon as well).
The real world doesn't map to the game board very well. Don't try to make sense of it - it rarely works properly.
The size stats for the sailing ship mostly match up to that in the range of a full-rigged pinnace or caravel, which typically only carried about 6 to 12 guns on average. Alternatively it could be a two mast trabaccolo, but they usually only carried two or three guns at most. At best the stats given would qualify as a sixth-rate ship of the line corvette, frigate or post ship under the royal navy rating system used in the Napoleonic wars. More likely they'd be classed as an unrated sloop-of-war, either a two-masted brig sloop or a three-masted ship sloop. At least, that's what Wikipedia has to say, since I'm no expert on nautical nonsense.
Ultimately, the stats aren't anywhere near that of a galleon or first-rate ship of the line. It's more in the range of a merchant vessel that someone's crammed full of cannons instead.
Yah, Paizo's "warship" (10 siege engines on each side, crew of c. 160, movable by oars as well as sails) is really a Napoleonic brig, not even a frigate (in the 28-44 gun range).
A 10' square works pretty well as the operating space needed for a ship-mounted gun -- the carriage is about 3-4' wide, with crew on each side, and the gun having enough space to recoil when fired -- but I don't think much thought went into how siege engines were actually used on board ship. (In particular, the idea that trebuchets could be used on a sailing ship makes no sense - they need a high arc of fire and you'd basically shred your own rigging any time you used the thing above decks.)
But then the Paizo system is mostly intended to let PCs heroically storm on board enemy ships and/or do clever maneuvers with ships; it's not remotely indicative of how real naval combats worked, either in the galley era or the gunpowder era.
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For information
Using HMS Trincomolee a real age of Sail fighting ship a 38 gun single decked frigate. Was armed with 28 18 pounders on her Gundeck , that is 14 on each side on a ship 150 feet long on the Gundeck, having been onboard her that is a very crowded feel and the spacing of the Guns was based on a lot of practical experience on how best to place the guns to allow the crews space to operate them. You may be able to place smaller guns slightly closer together . This also needs a crew of over 300 to sail and fight effectively
You can find photographs of HMS Victory, HMS Trincomolee, HMS Unicorn and the USS Constitution on line easily this shows you how the gun deck of any fighting ship should be laid out. The three Frigates are the sort of ship which utterly crushed pirates as none of them could afford a ship with a large enough crew or number of cannon to match them. HMS Victory is one of the largest Ships of the line to see action (the spanish had at least 1 larger ship and after the Napoleonic wars increased use of metal bracers on hulls allowed larger ships) ,
Ships are cramped. As a sailor on modern warships, whenever I'm watching a movie/tv show that involves a ship, I immediately notice how much empty space there is. If there is a lot of empty space, I know it is an artificial set. I worked on an aircraft carrier, which is an incredibly roomy warship. I'm 5'11 and I had to duck my head pretty regularly to avoid hitting it on things.
Right now I live in a 530 sq/ft apartment. If I were to lay it out like a berthing compartment, there'd be enough space for at least 18 people to sleep, possibly 24, because the ceilings are pretty high. And that's without converting the bathroom or walk-in closet.
Lots of helpful responses! One thing that recently crossed my mind is that perhaps the crew of a siege engine is actually supposed to occupy the same space as the engine, which is why the cannon and ballista are considered to be 10x10.
The crew serving a cannon are certainly standing closely a round it during reloading, less so when they run it out to shoot.
https://www.youtube.com/watch?v=mQSBxQiLSyQ
is a video of Gun Drill on the USS Constitution , for a fairly large (24 pounder only ships of the line ever carry anything bigger) which should show where the crew are
To Echo Irontruth the sailing ships have even less headroom than modern ships, On a modern ship I have occasional problems when going though watertight hatches on the sailing ships on the Gun deck as long as I pay a bit of attention I am ok, but on the decks below I bash my head on the crossbeams unless I stoop and I am shorter than he is.
But historically people were on average shorter when the sailing ships were built about 4 inches shorter on average than today , so I am not sure if that is a structural limitation or a design choice.
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JohnHawkins has it right based on my information as well.
Gun decks on a frigate tended to have low ceilings so they presented less of a target to the enemy. Thus the 7'4" for the USS Constitution measuring from the bottom of the planking to the bottom of the planking would lose a few inches for the planking and more for the beams making it comfortable only for short people like myself (net 5'-6' for the most part.
Looking at gun carriages they were maybe triple the outside diameter or the gun (based on diagrams from https://www.history.navy.mil/research/library/online-reading-room/title-lis t-alphabetically/c/the-constitution-gun-deck.html
For spacing, looking at a side view of the USS Constitution it appears to have a gun port roughly every 10 feet, so even cannon would likely take up 10'x10' if not more space on a deck.
When you look at how some game systems determine tonnage via 5' squares a ton becomes 5'x5'x5' cube of space. How many people can you sleep in a 5'x5'x5' space? About four on hammocks, possibly 6, but 4 would be more comfortable. Four gives you 18"-24" width space for each man (with 1'-2' extra space between) and 24" clearance between men above and the ceiling, whereas 6 men per is either 18" shoulders touching or as above but only 18" between men, or about 9"-12" clearance between men laying flat and no ability to lay on one's side or turn over. Wherever possible men would string hammocks, even above the guns, especially if you can fit more men between the guns and others over them.