Difference between a class inside Main class, class outside Main class, and class as Main class?

Here is the pic,
https://imgur.com/a/ZyobdG1
Is there a difference between a class inside the Main class, that same class outside the Main class, and that same class as the Main class itself?

 

Usually you would nest a class inside another to restrict the scope. If you want Count to only be accessible within BoardManager you could make it private/protected inside BoardManager. I also nest my classes/structs sometimes to organize my data, or if I'm too lazy to make a new file.

The last two images you shared are exactly the same. It actually doesn't matter if they are in the same or separate cs script files (though it's generally best practice to have them in separate files).