As a diabetic I can tell you that cottage cheese is low in sugar, while
yogurt (even "sugar free") is loaded with sugar (usually 15g for "sugar
free", 30g+ for regular) so from that prospective it makes perfect sense.
All of induction seems to be geared to keeping the carb count under 20g and
loading the foods toward those that metabolize slower.

Aged and fresh is one category.  Fresh cheeses are like cream cheese,
cottage cheese and so on.  Almost all varieties of cheese are aged.
To tell the difference, you have to know a little about how the cheese
is made.  If you've ever gone on a tour of a cheese making factory,
they mention that such-and-such a cheese is pressed from the curds
and then sent to a warehouse to age.  Bingo, such-and-such a cheese
is in the aged category.  Much of the time fresh cheeses are made by
the same companies that sell cream, sour cream and ice cream because
fresh cheeses don't need a warehouse for aging.

Once you know how a cheese is made, it's easy to tell a fresh cheese
from an aged cheese, but who knows how any one type of cheese is
made unless you remember a factory tour, work in the diary industry,
are a member of a gourmand club, etc.  I like factory tours, have
relatives in dairy farming, and have been a member of a gourmand club
in the 1980s, and I still don't know all fresh cheeses from all aged
ones.

Here's the Atkins issue: Aging consumes carbs, so aged cheese maxs
out at 1.0 per ounce and goes as low as 0.1 per ounce.  Fresh does
not have a chance to consume carbs, so fresh cheese can be milk that
has had the water drained out of it with a side effect of concentrating
the natural milk sugar.  "American process cheese" is the exception
that proves the rule here, it can be as high as 3.0 per slice.  Must
not be aged much.

Degree of hardness is another category.  Degree of hardness *only*
applies to aged cheeses.  They range is soft, semi-soft, semi-hard
and hard.  Sometimes there are more gradations, sometimes less.  It
mostly depends on what types of aged cheeses a company produces.

Once you know if a cheese is aged, and when in doubt figure it's
fresh, but at least anything with the word aged on the label works,
then it's time to figure out where it is in the hardness spectrum.

Here's the Atkins issue: Aging hardens the cheese in addition to
consuming the carbs.  You can figure out the hardness of a cheese
by squeezing it.  Easy to squeeze with your fingers, soft, assume
it is maxed out at 1.0 per ounce.  Pleasantly soft but it takes a
knife to slice like cheddar, assume semi-soft and maxed at 1.0 per
ounce.  Aged cheddars may well be lower but I'd have to look that
up because it isn't something I can get from this principle.  If
it can be easily sliced with a knife, like swizz, it's semi-soft
and you know it's under 1.0 per ounce but need to look it up to
find out how much less.  If it needs to be grated because it's too
hard to slice with a knife, then it counts as a hard cheese, and
you can expect it to be far below 1.0 per ounce.  The best real
Parmagiano Regianno that's rock hard is only 0.1 per ounce, and
delicious, and expensive.

What animal it comes from is yet another category.  Either fresh or
aged cheeses can be made from milk, and milk can come from: cows,
sheep, goats, water buffalo (the finest mozzarella) and for all I
know every other sort of milk-giving herb animal ever domesticated.
The fact that I've never seen camel or llama milk cheese doesn't
mean it can't be found somewhere in the world.  But is it one or
two hump camel cheese?  Heck for all I know some farmer in Finland
has figured out how to make cheese from reindeer milk and someone
in Alaska has figured out how to strap a muskox down long enough to
get milk from it (they are usually grown for their superior fur and
the wool) and make muskox cheese.

See that's a mix of 3 fresh ones (cream, cottage, mozz), a semi-hard
(swiss) and a semi-soft (cheddar).

Right, and if it says zero it's rounded down from 0.5 per serving.

Or unless you know how the product is made and what it is made from.

Heavy cream is allowed, sour cream is made by putting enymes into
heavy cream to thicken it, so sour cream can be treated like heavy
cream.  One you know how it's made and what from.

Yogurt is made from fresh milks or cream or skim milk.  It's fermented
with a different bacteria than cheese.  The yogurt bacteria eats fat
rather than sugar, so yogurt keeps its milk carbs.  And that's certain
to be an over-simplification, too.  But that's why yogurt doesn't
appear in lists early on, even in addition to the fact that fruited
yogurt has a ton of added sugar most of the time.  On the other hand,
yogurt bacteria is one of the beneficial types in our intestine, so
yogurt is very healthy in its own right.  But it sure makes me wonder
how anyone first got intestinal bacteria into milk and then ate the
sludge it turned into ...

Dr A's medical skills did not extend to writing.  A shame.  All manner
of misunderstandings come from that fact.  Everything from stressed
dark tests on the sticks to using weekly loss rates to determine CCLL
on are all problems created by his terrible wording choices.