@ES808 Great question!
No, standover height is different that minimum seat height. Standover height refers to the height of the top tube (the tube running from under the seat to the handlebars) from the ground. Another way to think about it is the height of the bike if you leave the saddle/seat and stand over the frame of the bike with your feet on the ground.
All of that is to say, that the 'minimum seat height' is not typically listed as a measurement for bikes as it depends greatly on the frame style and length of the seat post. The minimum seat height will always be several inches higher than the standover height. If you want your son to be able to sit on the seat and easily touch the ground with his feet then you will likely need to go with one of the 20" bikes.
As an example to illustrate: my daughter is 50" tall and has an inseam measurement of right about 22.5". She rides a Salsa Timberjack 20 Plus bike with the seat about 2" above its minimum. When sitting in the saddle, she can touch the ground with her 'tippy toes'. When she comes to a stop she has just enough reach to put her foot down and balance. To translate that to your son's experience, he would likely easily fit a 20" bike in that style. It would definitely be a stretch for him on a 24" bike.
Hopefully that answers the question for you!