“All are not” versus “Not all are”

Another issue of “Jim’s Pet Peeves.”  I think people understand the difference between “all are not” and “not all are,” but use “all are not” to mean both things?  At the Garden Center today I was reading a little blurb about succulents, which said in part “All cacti are succulents, but all succulents are not cacti.”  Huh?  I think they meant “…but not all succulents are cacti.”  And this in an educational brochure.  I regularly see this mistake in print and hear it on radio broadcasts, and I wonder if the journalists (writers and editors) actually understand what they are saying.

The first time I tried to explain this difference to somebody, I chose as my example sentence the obvious falsehood “All lawyers are not crooks.”  Changing “all are not” to “not all are” results in the somewhat less suspect “Not all lawyers are crooks.”  Perhaps that wasn’t such a good example after all.

When people say “all is not lost,” are they really trying to say “not all is lost?”