I first learned how to make ladderback chairs based on Alexander’s book, Make a Chair from a Tree. Then later, I studied a thin slice of furniture history from the perspective of those who made it. So what I know, or think I know, is pretty narrowly focused. There’s lots of kinds of chairs; generally I break them down into two forms – Joined chairs, like this one:
And turned chairs, like this one:

For now, I’ll concentrate on turned chairs. Whether they have a board seat, fiber seat; spindles in the back, or slats – the common feature they all have is the round mortise & tenon joint. I think of JA’s chair as a turned chair that isn’t turned. Alexander’s earliest chairs were turned; here is a one-slat Alexander chair all in hickory, with a paper imitation rush seat. Made c. 1974.
By 1976, Alexander’s chairs parts were shaved with a drawknife rather than turned. There is a long tradition of “un-turned” turned chairs, some reaching back to the 16th & 17th centuries. One helpful reference I found when studying London records was this, from the Company of Turners:
“20th February 1615 It was directed that the makers of chairs about the City, who were strangers and foreigners, were to bring them to the Hall to be searched according to the ordinances. When they were thus brought and searched, they were to be bought by the Master and Wardens at a price fixed by them, which was 6s per dozen for plain matted chairs and 7s per dozen for turned matted chairs. The effect of such an order…all chairs which came into London had to be submitted to the Company and if approved, were taken over at the fixed price. The Turners reaped the benefit by the removal of possible competition.” – this quote is from The Worshipful Company of Turners of London – Its Origin and History A.C. Stanley-Stone, (London: Lindley-Jones & Brother, 1925)
My italics. If “plain” matted chairs are distinct from “turned” matted chairs, then I conclude they aren’t turned. “Matted” refers to the fiber seat, usually rush. Paintings & prints are helpful to a degree in seeing what sort of chairs were in use at a given time. There’s loads of examples. This painting by Cornelius Decker (1618-1678) shows a 2-slat shaved chair in the lower right corner.
Looking at it in detail, I see a few things. Square posts (well, sometimes they’re rectangular, but not round, thus “square”). Only 8 rungs, and the lower ones are quite close to the seat rungs. Doesn’t offer much strength that way. Either the chair has wracked so the rear posts are now canted back, or it was bored to achieve that. Rush seat. Moving those lower rungs down would strengthen the chair.
Meeting in a tavern, by De Jongh (1616-1679)
The chair in the lower right hand corner, has some perspective problems. But we can see several details. Might be 12 rungs, it’s at least 11; through mortises; a cushion; square posts.
this detail from Michiel Sweets’ (1618-1664) “The Academy”: 8 rungs, through mortises, rush seat, 3 slats. No bend to rear posts. Small chair.

A mezzotint by Wallerent Vallaint (1623-1677). This is a detail; all we can tell is the chair has square posts, round side rungs, through mortise for a very tall slat. Either intentionally bored to cant the rear posts back, or wracked to just-about-falling-down.
Same artist, different chair. Note the raked rear post, clearly shown here. I’m of the opinion this is intentional to give the chair a bit more comfort than if it were bored so the rear posts were plumb. This time, two rear rails, with turned spindles between them. Discard any notion this chair was shaved/square posts because there was no lathe! Very low seat, allows you to work easily in your lap. Only 8 rungs. Rush seat.

I made lots of shaved chairs in the years when I wasn’t making JA style chairs – mine were more like these period-style chairs. I could make the chair frame in a day, maybe 6 hours. The rush seat took me as long or longer! This one is maple posts and white oak slats. Rungs might be white oak or ash. Rear posts hewn above the seat to cant them back just a bit.

more of this sort of stuff here; Alexander, Trent & I (mostly Trent driving this article) on shaved chairs – http://www.chipstone.org/article.php/581/American-Furniture-2008/Early-American-Shaved-Post-and-Rung-Chairs