I don't know if "modern european" is a good way to put it, I kind of think it's a result of the cold war, never made a lot of sense and was enforced by the arrival of neo liberal ideologies in european governments afterwards but that part is just a quick throught so don't quote me on it. You are definitely right that there are different definitions tho, one of them just also seems to reframe the word liberal which makes absolutely no sense to me. In the end they are all flawed and the biggest issue is that no matter which you use extreme ideologies like neo liberalism and backwards thinking aka the "modern" definition of conservative attempt to frame themself as the "middle" which is dangerous af and makes no sense ether so it's a rather pointless fight with a third party as winners! :/