In article , Jos Bergervoet
writes:

Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"

Right. Tegmark does use the term differently than most people, but he
does define his terms and use them consistently.

Wchich nevertheless makes things unnecessary confusing.
Tegmark damages his own cause by reverting to this kind
of word game. (Unless his cause is just to create a
spectacular picture to make it into the news headlines.)

I think his reason for this is to have his Level I multiverse be
something which is essentially mainstream; that might make the other
multiverses easier to swallow. From his point of view, everything which
is not in principle observable now but nevertheless exists is in some
level of multiverse. Thus, it has its own inner logic.

Note that some people have used "universe" to mean "all that exists",
by definition, so even without Tegmark the terminology is not uniform.

Yes if you define a *new* concept. But you do not
need to deliberately use novel names for existing
concepts (suggestive names that sound interesting,
as Tegmark does with his "level I multiverse").

If that were it then, yes, it would be as silly as calling it Joe.
However, in a book about the various levels of multiverse, it does have
its own logic.

I wonder if the same happened with "world" after
people realized that there are other planets..
Especially after Newton's unified theory of forces
either on earth or far away from it, there might
have been a sense that everything now belongs to our
"world." (And the opposite view, that world should
just apply to our own planet, apparently won.)

To some extent, yes. "Plurality of worlds" was once taken to mean not
just other planets, but other systems including fixed stars, planets, a
central star etc.