I'm going through the same thing recently, and had visited the hardware store three times to get the right item as none of the in-store helpers know the answer to what size to get for a certain size knockout. Apparently I am one of those who didn't bother to take a sample on my shopping trips. Lesson learned. My bad.
I'm just a regular diy homeowner, and I'm not saying what I shared below is definitive nor authoritative. If some information is incorrect, it's mentioned unintentionally. Posting false information is the last thing I want to do. So, don't grill me please if I'm wrong.
The information I gathered is from multiple trade organizations and agencies.
First, it's important to understand the concept of nominal size, trade size, actual size, OD size and ID size.
Nominal size and trade size are NOT actual sizes. Just like 2x4 is not exactly 2" by 4".
Also try to remember that these standards were started many decades ago, and situations tend to change slightly over time.
I don't exactly understand why the trade uses this way of specifying sizings, but I think the logic is that an electrician doesn't have to dig through the codes to find out what actual size of fittings he/she needs to purchase if he started out with a certain size cable bundle.
It seems that, as far as connectors matching knockout goes, the diameter sizings are dictated by using EMT as the usage case. This is simply because we are focusing on knockout and connector sizes here. The different usage for EMT, NM or MC cabling only means different methods of fixing the cable to the connectors.
A 1/2" trade size conduit means that conduit size is for cabling up to 1/2" diameter. The actual OD of this conduit is larger than 1/2".
There's then a standard dictating what hole size is required for this '1/2" ' conduit to go through. And that is a 7/8" actual size hole.
3/8" and 1/2" seem to be interchangeable. The conduit standard doesn't seem to have a 3/8" size that I can find. However, there seemed to have 3/8" sizing for flexible metal sleeve cabling.
In the same token, a connector marked as 3/4" should be used for a knockout hole with approx 1 1/8" diameter actual size.
So there you go. These are reasons why they are marked this way. Again, I could be wrong, but I believe I'm fairly close. Hope this helps