> ISBN10 (which can be converted into ISBN13 without anything else IIRC)
Yes. There clearly only needs to be one way to identify things, so commonly larger systems just incorporate the smaller ones wholesale. The 13-digit system just incorporates the prior 10-digit system for International Standard Book Numbers with a 978 prefix called "bookland" (most prefixes in this system are geographic, but of course books aren't really from one single geographic region, so they're from "bookland") and adds a new set of possible codes. It also incorporates the entire 12-digit American "UPC" system.
Several other (less well known) systems were gobbled up the same way as "bookland", just allocating them imaginary geographic regions in the 13-digit system.
There's actually a fourteen digit system, but the lead digit tells you about how many of something are bundled e.g. so a distributor can distinguish a truck full of Pepsi cans from just one case or a single can in terms of things you can order. Lead digit 0 means "single" so if you know the 10 digit ISBN you can not only make a 13-digit EAN for that, you can make the 14-digit GTIN that means "just one of this book" which in most cases would be what you want.