True. There isn't even a single "family" or "class" of stainless steels, but several: ferritic, austenitic, martensitic, and duplex (a combination/hybrid of ferritic & austenitic). Actually, these are the "families" of stainless steals classified by microstructure. Precipitation-hardening stainless steels are generally considered a 5th family. There are subclasses of these 5, too.
On the other hand, almost all corrosion resistant/stainless steels are alloys with a (relatively) high chromium content. In general, they are defined alloy steels with ~11% chromium content or higher.
Probably true for all practical purposes, but being the annoying stickler I am I can't help but add some qualifiers. Like any alloying element, the addition of chromium has an effect on the microstructure of stainless steels, including the corrosion resistance for which high levels are added in the first place. Another effect, however, is embrittlement. In general, there is always a trade-off between "toughness" and "hardness", which speaks to this:
The "harder" a knife, the greater the edge retention. Any good knife-maker/seller will tell (or already have listed in whatever online or printed catalogue you're looking at) you how "hard" the blade of a particular knife is on the Rockwell scale. Tactical knives, workhorse blades (e.g., high end machetes or other knives that are large and used to chop brush or other high-impact purposes), most hunting knives, etc., typically are hardened to between 55-57 RC to 57-58 RC.
It is possible to take just about any steel and harden it to 67RC or more (which is insanely hard). However, there is a reason that the co-developer Chris Reeves of CPM S30V & S35V steels hardens his coveted
Green Beret tactical fixed blade to 55-57 RC, and many kitchen knife made from inferior steel is ~60 RC: the harder something is the more brittle it is. The RC scale itself is based upon diamonds, the hardest naturally occurring substance, meaning it will cut pretty much anything but you can shatter it with an iron hammer.
Likewise, the harder the knife's edge, the more likely it is to shatter. Different steels that are just as "hard", though, are not equally brittle. Thus kitchen knives and some pocket knives hardened to 67 RC are just as "tough" as kitchen knives made from 440C, VG-10, CPM-S30V, 154CM, etc., but are much harder and therefore keep an edge much longer.
Chromium embrittlement itself is classified into e.g. 475c embrittlement (c = degrees Celsius), sigma phase embrittlement, etc. Basically, the addition of the amount of Chromium necessary for a stainless steel allows the formation of precipitate phases in a particular alloy that are structurally "weaker" or more simply are brittle.
More generally, the mechanism whereby the addition of chromium creates a corrosion resistant alloy is passivation or the ability for surface layers to form into an impermeable film that isn't possible with other alloys. However, this mechanism creates the possibility for various
structural corrosion, and in particular stress corrosion cracking (SCC). There is some debate over the exact nature of the mechanisms underlying SCC in stainless steels, but the important point is that the addition of Chromium has a variety of effects not only on what precipitate phases can occur when the steel is formed but also how it will react to thermal, chemical, and mechanical variables.
For example, anybody familiar with knife-making or blacksmithing in general is almost certainly familiar with heat-treating as well as quenching. Both (related) processes are central to "hardening". Ferrite stainless steals can't be heat-treated. Martensitic stainless steels, which include perhaps the most common blade steels (the 440 series- a, b, & c), can be heat treated. However, there is still a limit to their strength "range" that hardening and tempering allow.
Just like the trade-off with hardness vs. toughness, there is in general a trade-off between corrosion resistance and structural integrity.
Spyderco's Sharpmaker comes with two sets of sharpening rods. The first pair are made of the same material your regular, ol' pocket-knife sharpener is. The second are artificial sapphire. They are extremely hard, but
1) not as hard as diamonds
&
2) very fine.
They'll cut any steel, but unlike most diamond sharpeners they won't strip away too much steel in the process. Blades aren't typically very "hard" (or, in the case of differentially treated blades like traditional Samurai swords, the edge isn't very hard) relative to numerous other materials including standard grinding/sharpening stones. It's just that high-end blades tempered/hardened to ~60 RC or more can take an insane amount of time to sharpen using your average stone. That said, there are plenty of high-end, cutting-edge (bad pun intended) stones & rods that are better than diamond sharpeners, last longer, are more forgiving, and improve the longevity of your blade.