

The first subdivision would be hand-made versus machine-made. Apart from maybe a few 19th century stamps, ALL stamps are printed on machine-made paper.
The textile-binding of the long wire/sieve gets imprinted in the paper-reel at the wire-side and hence maybe visible in our stamp papers.
This sieve-structure has (so far) 3 types of binding:
Linen-binding:

after connecting the cross-overs by a blue line:

Twill-binding:

after connecting the cross-overs by a blue line:

The purples lines represent diagonals our eyes are less likely to see, but still!
In the linen-binding the diagonals are symmetrical and are equidistant - the next parallel blue line is just as far way in the case of the ascending lines as of the descending lines.
In the twill-binding, however, the ascending blue lines are nearer to each other!
I hope this will make it clear why I refer to the linen-binding as symmetrical and to the twill-binding as asymmetrical. It is not just the angles of the blue lines but also the density!
The first two types of bindings can be found chronologically since the 1850-ies till 1937 with NO exception. ALL have a linen-binding.
The twill-bindings can be seen since 1937 - occurring for the first time in Canadian stamps.
Around 1971 the "simple" bindings were replaced by a multi-layered binding.
There is NO laid paper as coming from the long sieve! It is either a watermark OR a later finishing-off the paper-reel that is responsible for the so-called "laid lines".
The is NO wove paper as such! ALL machine-made papers have a weave-like pattern [see my pictures above!]
Whether the sieve structure becomes visible for us depends on a variety of factors. None of which justify a separate category of paper!
The so-called "ribbing" is NO extra effect but depends on the relative thickness of the threads of the sieve.
Having established the direction of paper - i.e. where are the lengthwise threads of the sieve - and placing a stamp in our hands so the lengthwise threads run vertically, the horizontal threads are sometimes thicker. In a linen-binding this will rarely give a visible effect, in a twill-binding these thicker line give us the impression of "ribbing"!
ALL "ribbings" in Canadian stamps in the 1952-1975 period come from the twill-binding. Although it may be expected that the best side of a stamp paper - i.e.the felt side - was used for printing, this is NOT always so!
ALL 1952-1955 stamps have the wire side printed!
In the 1955-1967 period most stamps on uncoated paper have the felt side printed.
Since 1967 it gets complicated, too complicated to go into it in this thread....