A privateer is not a ship type but any ship operated by private individuals, or a group of them, for profit. They are given the right, via a letter of marque, to engage in acts of war on the seas by their sovereign power, which takes a percentage of any captured prize. Profits are otherwise split among crew and owners. The possession of the letter of marque, and the return and sale of prizes to the sovereign power, is what distinguishes a privateer from a pirate.
Not surprisingly, some pirates sought the letters (often illegally) to absolve their actions. Others acquired letters from opposing countries at war (not admitting to this, of course). They then attacked both sides as desired. For example, a privateer might have letters of marque from England and from France, using the former against French ships and the latter against English. Only he and his crew, and possible owners, might know this.
Privateers who didn’t return captured prizes, or who otherwise violated their agreement, could be declared pirates. Some countries refused to recognize the letters of marque from their enemies and hanged captured privateers as pirates, or at least threatened to, leading to negotiations for an exchange of prisoners, for example.
As for the ships, they were heavily armed, fast, and highly maneuverable, as they were intended purely for assault. Since they captured ships and sailed them back (treasure inside), there was arguably less need for their own cargo space beyond provisions. Anything larger than a frigate was unsuitable (i.e., no ships-of-the-line).