They do mean the same thing. In fact, you could also say "If you add 3 and 5 you get 8".

I'd think of them like this: If you are eating at the moment you are talking, you would say "I am eating" (Present continous). If you are about to eat, or know a time in the future you will eat, you would say "I am going to eat (in 5 minutes, on Tuesday, next year etc). If you know you are going to eat at some point, but not when, you would say "I will eat (in the future). You can say "I will eat in 5 minutes" or "I will eat next year", and these are fine, but if you just say "I am going to eat" without any time indication, the people you are talking to would assume you mean almost immediately (well, I would anyway!).

First notebook entry: Introducing myself

Ciao! Mi chiamo Mike. Ho diciannove anni. Sono inglese. Abito a York. Sono studente di matematica. Mi piace il calcio (Mi piace la squadra del Milan :). ), i giochi (il computer, PS3) e ascoltare la musica. Conosco un pò di italiano. Vorrei studiare di piu l'italiano.

How beautiful it'd been.

I would not have lost you. I would not have lost us. I would have not come back home that day in which we were over. You know neither of us that day wanted to accept what was happening. How long did we stay together hugging each other ?
Anyway I'm happy without you. I can live without you. I don't need you. I think since we've broken up I've grown more mature without your help but you know, I think you have influenced me, drawing a little piece of my path. I'm sure about it. You are not important for this reason, because all the people who I meet every day, they influence me a little bit. It's a good thing. It's like a lovely puzzle. I'm a puzzle made by lovely pieces. One by one they are gonna start drawing out my personality, my ideals, myself.
So, the only thing which makes me upset is that since that day I still haven't found someone with whom I can speak about everything, with whom I won't be embarrassed if I start to tell them about my fears when I was little or about my trips, my problems, my dreams.
To be honest, one time I met a guy with whom I could speak about these types of things, but the fear between us and to going towards new things scared us. It was lovely company, just for a night. A really lovely company. But look, I told you, the fear was stronger than we were.
And maybe the faith was too, that you would decide to come back to me, in the time in which I was supposed to think about other things instead of you.
How beautiful would it have been had we had continued our path? But I suppose we were looking away, not in the same direction. Actually, you were.
I don't hate you. I love you, but I don't really LOVE you as if we were engaged. It's a different feeling from before.
Do you think we are running in circles? After two years? After new experiences? The way we always try to not lose ourselves? How we are maybe like the Endless Knot ? Maybe I will answer to my joy, my Nirvana, break it. What do you think ? It could happen. Because I swear to you, I don't need you. But I still love our talks. Platonic Love.