Do different types of paper with the same weight necessarily have the same thickness? For example, does 300g card stock have the same thickness as 300g photo paper, or do papers vary in thickness according to their type?
Short answer: no
The two different types of paper with the same mass would only have the same thickness if they had the same density.
Photo paper would have a much higher density than card stock, so 300gsm photo paper is actually quite a bit thinner than 300gsm card stock.
300gsm card is actually quite thick:
Whereas 300gsm photo paper (shown here: 300gsm luster paper) is actually quite thin:
The best example that I have found so far is this:
Even if we take into account the slight difference in the grammage, the latter paper is more than 60 % thicker.
(Caveat: There are many different ways to measure the thickness of a paper. The above examples are from the same web site, so there might be at least some reason to believe they are comparable.)
300 Grams paper means: An A0 sheet of paper (1 m2) weights 300 grams. So essentially the thickness is not mentioned in here.
I think that the thickness of different types of paper of the same weight (matte, glossy, etc) do vary a bit, due to chemical treatments of the paper and/or different production methods/materials, but not very much.
While, on reflection, that's an almost trivial statement, it's also more useful and (a little) profound than may at first be obvious. Read on ...
In the following text the following common conventions are used.
"m^2" = "square metres" and
" ... /m^2 = "per square metre
gsm = grams pr square metre
g = grams.
so g/m^2 = gsm.
Affect of density on thickness:
As others have noted, for a given number of grams per square meter a material's density will be inversely proportional to its thickness. ie for a given area
A fluid example:
Consider this non-paper example to remove irrelevant aspects from consideration.
If you have a 1 m^2 (=one square metre) "pan" (with walls taller than maximum fluid depth used. containing water 10mm deep (1/100th of a metre) then the water will have a "weight" of 10 kg per square metre - so there will be 10 kg of water in the 1 m^2 pan.
If we instead used Mercury with a density of ABOUT 13.5 times as high as water, to get a weight er area of 10 kg per m^2 we'd need a mercury layer of 10mm/13.5 = ABOUT 0.75 mm of mercury to get 10 kg/m^2.
*Paper - The Axx sheet size system - the magic factor.*
If we stick to gram / square metre paper weights, and "metric" (A0 A1 A2 A3 ...) paper sizes we discover some simple but useful magic which many people are unaware of.
As is well enough known:
If we fold a Sheet of A0 in half it gives an A1 sheet size
Nothing too magic so far.
Still no magic.
Some enlightened souls decided on the following system:
As above, a sheet of A0 has been defined to have an area, by definition, of exactly one square metre.
is 2 raised to the power of the sheet size.
k = 2^ N for AN sheet size.
For a sheet of A4 the divisor = 1/ (2^4) = 1/(2 x 2 x 2 x 2) = 1/16.
For A*N* paper
So for eg A3, 70 gsm paper