Yes, there are different grades of stainless steel.
Most cutlery is 316, 420, or 440.
I disagree that you'll find cutlery in 316. That is usually a pan/pot steel with lots of nickel and very high chrome. Also often used for sinks, restaurant prep surfaces and so on. It won't harden enough to be a good knife.
Otherwise, Aunt Bea's post is useful.
Most of the Henkels/Wusthof types are something like XCrOMV15. You'll also now see lots of Chinese steels like 8CR13MOV These are all OK, usually hardened to 56-58 Rockwell hardness--RC is the common abbreviation. It's a good balance between hardness and toughness.
What does hardness mean? It's a tradeoff between hardness and toughness. Something at 56 hardness will be easy to put an edge on but not hold it as well as something harder. However, the 56 hardness steel will be more resistant to chips, cracks and so on compared to the same steel at a higher hardness
There are lots of higher grade chef's knives out there now that might go as high as 61 RC. Your average home cook probably will find that hard to sharpen. But if you have the waterstones and such, these are very rewarding blades.
You can also find lesser steels hardened too far. A well-meaning friend gave me an AUS 8 blade hardened to 61--at least according to the provided paperwork. That's overhardened in my opinion, being difficult to put a fine edge on but prone to chipping out too. AUS8 is respectable in that 58 range hardness.
If you don't want to dive into the arcane details of metallurgy, that's fine. Just talk with people like us here about what good values particular knives are.
I think there is a lot to like about Forschner/Victorinox at their price point.
I think Wusthof/Henkels are overpriced and too thick. Tojohiro, MAC are better values at those prices. The Wusthof Ikon line is OK, and so on.
Personal preference enters into it too. I don't like bolsters generally, but particularly dropped bolsters. They complicate sharpening and cutting unnecessarily. I prefer the flatter French/Japanese cutting profile compared to the curvier German. These aren't about right and wrong, just what you prefer.