Are you not susposed to run a 28c tire on 24 internal rims?
ETRTO guidance and UCI rules would say no—so as of mid last season this would be an illegal combination for racing on the basis of safety. While blowoffs are the catastrophic failure, the more common issue of too wide of a rim is riding on the sidewall and getting more punctures.
The C on tire sizes has nothing to do with width—it’s the designation for the bead seat diameter (BSD) of the rim (622mm). The format you all are seeing are looking at is referring to the different dimensions of the rim. 700 is a size designation that is supposed to the OD of the system at some arbitrary tire size that was historically used. The only place where this is still relevant is for 650b vs. 650c. Tires are specified in the format of [size designation]x[width][BSD].
Actual tire width for road tires is specified on a different rim width thats sort of standard and sort of manufacturer dependent. Most 28s are specified for a 19mm or 21mm IW rim for example and most 32s are to a 23mm or 24mm IW rim. 34+ is usually true to size on a 25mm IW rim.
To make matters worse there are two different ISO standards for tire clearance to the frame. 6mm is the off-road standard that gets used on a lot of allroad and gravel bikes. Some manufacturers (e.g., Trek) use 6mm on their road bikes too. 4mm is the road standard that also sometimes gets used for allroad and gravel bikes.
If you want to make sure a tire / rim fits your bike the best thing to do is measure or get a dimensioned drawing of your bike frame to compare. Most fork and frame manufacturers can provide this if its not in the listing.
TLDR: for road widths 23mm IW width rims give you the most options. 24mm-25mm is good too as it allows you to fit 30s. Measure your bike and the tires. You probably want 4mm of clearance on all sides of the tire and similar to the rims.