The EU has a huge variety of plugs and sockets, what people often call the EU plug are variation of the schuko[0] design. The standard EU plug is the Europlug[1] which is compatible with most (but not all) sockets in Europe and only handles low amperage.

AFAIK Italy is the major outlier in having widespread sockets[2] that do not accept the Europlug

[0] https://en.wikipedia.org/wiki/Schuko

[1] https://en.wikipedia.org/wiki/Europlug

[2] https://en.wikipedia.org/wiki/AC_power_plugs_and_sockets#Ita... the one on the left, rated for 16A.

A tiny bit more complex: the German/European plug has the ground at the sides and so goes in both ways. The French/Belgian plug has instead a ground pin that goes from the socket into the plug (so the opposite of the other two). That means generally you'll be able to combine both and most products have a plug that allows to connect to both varieties. But there are some (especially Chinese and American) products which miss this diversity and either only fit in one of the two or produce local varieties for either one when it would well be feasible to produce a single version that fits both.