The difference is present tense vs. present perfect tense. I realize that => At this moment in time I am aware of it. (we don't know when I became aware of it, but I am aware of it at this point in time) I have realized that => At some time in the past I became of aware of it and I have known about it ever since. (could be minutes, months, or years ago when I realized it)

There is not much difference between the two sentences. Let's say "I realize that" is not related to any particular timeframe. It's just a very straightforward statement whereas "I have realized that" refers to some realization that started in the past but is still valid now. So, basically, the difference is related more to grammar than to actual meaning. Hope this helps.