In my life I have seen the same grammatical objects change names. Just imagine the confusion of a French child going through a system comprising 9 years of formal teaching of French grammar and seeing the same object named differently according to the teacher.

In France the teaching of grammar is at the core of the teaching of French as a 1st language, either officially or non officially ("teach grammar but don't say you do"). The Ministry of National Education has issued a list of official grammatical terms, I think this is the latest issue.

But walking from one classroom to another you will find teachers do not use the same terms (knowingly or not) and different terms are used when teaching a 1st or a 2nd language or the same language as 1st or 2nd. The tradition of teaching grammar is quite different in Britain (I can't speak for certain for other English speaking countries but I suspect it is not much different)

not only because grammatical objects are seen from a different perspective, but also because the teaching of French grammar has until rather recently (I expect a century or thereabout) been influenced by the teaching of Latin grammar, a lot more than English has.

ll of this aside the terms used nowadays in FLE (Français Langue Étrangère) books conceived by people who have carefully thought it out and who care about didactic methods are much more reliable than most of what you will find on the web as those you name in your question, even if they will also sometimes name things differently.

@None Did you happen to read what I wrote in my comment? The confusion seems to stem from nomenclature. Silph mentions personal pronouns but not impersonal pronouns. If you look at this from that point of view, the issue goes away. Thought company divides its explanations into two sections. That's all.

I can't imagine that basic stuff is taught in different ways in different countries.