PU (not PE) glue in liquid form is straw to tan colour. In semi-solid form (sold as tubes for caulking guns) it is white and it comes out of the tube. You are probably familiar with a related glue - heat activated PUR. This is the glue used on the back of iron-on edging tape etc
Yellow glue in the USA is an aliphatic resin, a modified PVA (it is all fundamentally modified corn starch). In the UK it is relatively expensive given that it's performance is no better than home-produced PVA
PVA in the UK has differences. Here we talk in terms of glues being classes D2, D3 and D4.
D2 can be dissolved in water (or acetic acid) eventually and and so is only suitable for interior work where it will remain dry. Example: Evostik Resin W (green bottle)
D3 is cross-linked, so as it cures there are chicsl changes which occur that are irreversible. It is suitable for use in semi-damp environments not exposed to extreme weather, such as most exterior joinery. Example: Evostik Resin W (blue bottle)
D2 and D3 catagories generally apply to PVA glues
D4 is completely weatherproof and can withstand repeated soakings. This catagory was once the sole domain of the PU glues. In recent years modified PVA glues have achieved D4 ratings as well. In use the differences between the two are that PVA spills wash off your hands (hot water and soap) whilst PU reacts with the moisture in the skin, hardens the skin and makes it go black. It takes several days before you can scrub that black off. PU glue also foams, so you need to ensure that you don't use too much because it will foam out and mark your work. As said that foaming can blow joints apart unless they are mechanically clamped. Example D4 PVA: Everbuild D4 Premium Wood Adhesive (Toolstation, etc) : Example PU glue: Everbuild Lumberjack 30 Minute Polyurethane Adhesive (makes Gorilla look really expensive)
In general use you will find little difference in performance between a premium PVA glue and an equivalent premium yellow glues. The faster PVA glues set just as fast as aliphatic resin glues, meaning that there is no advantage to them in that way, either. And certainly for joinery and the like the only appeal I can see in the American glues is the snob value, because they are relatively expensive for what they deliver
In trade use the modern D4 PVA glue is so good that it has started to displace lower grades of PVA, some PU glues and traditional "permanent bond" adhesives such as UF (urea formaldehyde), e.g. Cascamite.
Sorry, long post, but rather than recycle a discussion on another forum I thought it better to hold the gen here
