How first- through sixth-rate warships were divided

Was every ship below 90 guns a third-rate?

No; third-rates were roughly 60-82 guns, second-rates about 84-98, first-rates 100 or more, and smaller ships fell into lower or unrated categories.

A third-rate generally carried about 60 to 82 guns. Second-rates occupied roughly the mid-80s through the high 90s, while ships of 100 guns or more were first-rates. Fourth-rates fell around the mid-40s to low 60s, followed by fifth- and sixth-rates. Craft below those categories were described as unrated rather than assigned a theoretical zeroth rate.