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Let's take a second to calibrate our eyes. This is a 12"x18" slice of chipboard. Each of the 4 sizes are based on fractions of this area.

A full sheet is XL.
Half of that is LG.
Half of that is MD.
And half of that is SM.

Here is that same 12"x18" slice - this time, with some familiar objects on it. That's a 12" ruler. Now, let's talk about some of the sizes, their functions, and ideal candidates for each size. By the time we're done here - you'll have it figured out, I'm sure of it. I've got a good feeling about you!

X-Large.

Let's start with the largest size and work our way down. The yellow sheet is 11"x17". XL can take up the entire sheet - basically anything larger than 9"x12" and any size up to 12"x18".

XL is art prints, posters, restaurant menus, signage, etc.

Common XL size:
11x14 - framable art print size
11x17 - poster
12x18 - poster
12x12 - record-sized print

Large.

This is a classic size on this side of the ocean - the imperial measuring system is proud to present - 'letter' size - 8.5"x11". LG can take up the half of the parent sheet - basically anything larger than 6"x9" and any size up to 9"x12".

LG is art prints, hand-outs, restaurant menus, generic print-outs, etc.

Common LG size:
8x8 - square artboard
8x10 - framable art print size
8.5x11 - standard 'letter' size
9x12 - max size

Medium.

Often referred to as "statement" size, this is about half of a 'letter' size. This yellow sheet measures in at 5.5"x8.5". MD can take up about a quarter of that original 12x18 sheet - basically anything larger than 4.25"x6" and any size up to 6"x9".

MD is invites, small art prints, oversized postcards, rack cards, etc.

Common MD size:
4.25x6.25 - A6 card size
5x7 - invitation
5.5x8.5 - statement size
6x9 - max size

Small.

I think of this as a quarter sheet - because it's 1/4 the size of a letter-sized sheet. SM is anything under 4.25"x6". That is a weird size to draw the line on - it should just be 4"x6", right? Well, that's correct, but that extra 0.25" has significance. 4.25"x6" is the largest postcard that you send using just the cheaper "postcard" stamp. This yellow sheet measures in at 4.25"x5.5". SM can takes up about a, eighth of that original 12x18 sheet - basically anything larger than a business card, and any size up to 4.25"x6",

SM is postcards, details cards, inserts, flyers, etc.

Common SM size:
3x5 - index card size
4x6 - postcard size
4.25x5.5 - quarter-letter size
4.25x6 - max postcard size

Other Thoughts

Square. Squares are weird. Based on the parent paper sizes that exist in my world, everything fits better as a rectangle. Squares are super do-able, we just need to cut off a little more paper.

Here are the largest size for each of the sizes:
SM: 4.25"
MD: 6"
LG: 9"
XL: 12"

If you ever have a size that you're wondering which bucket it would fall into, just ask - I'm here for it.

Smaller Sizes. 3 inches is basically the smallest dimension that fits into these sizes. 3"x3" would fall into the SM size.
A standard business card is 3.5"x2".
Our bookmarks are 6"x2"

Larger Sizes. 18 inches is the largest that I can print in this fashion. And if it's 18", the other dimension must be 12" or less.
Heavy bond can go up to 24"x36"... there is no cardstock option for stuff that large here.