European and remy are two different types of hair, remy is human hair from an Asian donor, and is thicker in diameter than a caucasians hair is.
Remy has lesser processing done to it than the standard processed hair so its color will last longer and is said to have more resistance to breakage.
Alot of places who do carry it wont charge extra for it but the problem is, alot of suppliers out there will tell you "sure, we can put remy in it for you" but then they just deliver the standard hair and you wont really know the difference unless you`ve worn a few of each before.
European hair is caucasian hair (from a European donor) and is also less processed than standard hair.
It is a finer hair than remy, and of higher quality as long as its authentic.
There are, of course, places that will give you what they "say" is Eurohair, but it isnt really.
One way to tell for sure if they are really going to give you authentic Euro hair is they`ll up the price VERY significantly since that is a much finer hair than the others and is quite a bit more costly.
One of the online suppliers insists on using ONLY Euro hair, and his hairpieces are in the 500-600 dollar range.
Virgin Russian hair is another one of the finer if not THE finest available, but few places will carry it and just the hair alone costs more than three times that of an entire hairpiece from most places.