I realised that the sky is blue. A statement that at some time in the past, you had this realisation. That is, it refers to a point in the past,when you had this thought. I have realised that the sky is blue. You, at this point in time, have already had this thought, previously. That is, it refers to now and talks of something that happened at a time before now. . At exactly 2PM last thrusday, I realised that .... . I have realised that ... and think we need to change things.

There are similarities because if you realized something in the past, it affects your present state of mind. After trying to speak English on my trip to New York, I realized that all my years of studying English in school hadn’t made me fluent. (I figured it out on my trip in the past) I’ve realized that you need more than classes in school to become fluent in English. (I came to this realization in the past, and I think that way today)