(First and btw, "Mod Podge" and also Royal Coat, etc, are just brand names for the thinned-down permanent-white-glue used for doing the process called decoupage. You can make the same thing by thinning down your own permanent white glue, like Elmers Glue All for example.)
Elmers is the brand name for a number of different glues, including "white glues" (there are other brands of white glue as well).
---Elmer's GLUE ALL is Elmers' *permanent white glue* (also known as "PVA glue," "craft glue," etc).
---Elmers *WASHABLE SCHOOL GLUE* is Elmers' non-permanent white glue, which will wash out *even after it dries.*
(Those both dry clear if thin enough and given long enough to dry thoroughly.)
I can't find the other two you mentioned:
...Googling "Elmers ALL PURPOSE Glue" just brings up Elmer's Glue All (it's "all purpose" in the sense that it can be used on various materials--usually porous or non-smooth materials and surfaces--and for various jobs). ...The only other mention of Elmer's All Purpose is for their glue sticks.
..."Elmers WHITE" brings up Elmers Glue All and Elmers Washable School Glue. Both of those are "white glues," though one is permanent and the other isn't.
(Elmer's also now seems to have a stronger permanent white glue, presumably to compete with other permanent white glues on the market which are generally thicker and stronger --e.g., Sobo, Weldbond, Crafter's Pick the Ultimate, etc, as well as "tacky white glues," etc which are much thicker...other permanent white glues are white "fabric glues," and those for gluing "gems" to fabric like GemTac/etc, and thinned down ones like Mod Podge sold for doing decoupage).
So I'd say that usually Elmer's Glue All is the "white glue" that would most commonly be used on flexible craft foam (the kind sold in colored, flexible sheets) as well as on polystyrene foams (inflexible, usually white, lightweight) which are also called "craft" foams though those foams are also used for more than crafts.
And Elmer's Glue All is also used for most other crafts where a glue of that type is needed as well.
However, neither of those types of "craft foam" require sealing at all since they're already waterproof and permanent (unless you want to put something else on them, like paint or decoupage, etc).
If permanent white glue is applied thinly enough (or watered down a bit), it will dry clear and glossy and be water-resistant with a bit of flexibility. In very humid conditions it could begin to look a little cloudy here and there, but will usually dry out again when put in dry conditions.
You can see Elmer's glues here:
http://elmers.com/products/glues-and-adhesives
P.S. "Permanent white glues" are technically PVA glues (polyvinyl acetate).
You can read about that kind of glue and see a list of all the kinds of glues by type on this page:
( http://en.wikipedia.org/wiki/List_of_glues ...for PVA glues, look under under "Synthetic Glues" then click on Synthetic Polymer Glues)
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