Whether I use random or random(), I 'seem' to get the same results. Now, coming from a Python background, using random() seems more natural and convenient to me, but I've seen random being used plenty a times.
Neither statements produce a hint or a warning using FPC's appropriate flags.
So, is there a difference, and if yes, what is it?
There's no difference. Pascal doesn't require the parentheses when calling functions without parameters. You can use them to make your code more clear when reading it, but they're entirely optional.