Questions and Observations for American Football Fans

[Spongebob]

I do not understand the difference between a kick going out of bounds on a punt, vs a ball going out of bounds on a kick off after a score. Isn't the idea to put  back the receiving team up as much as possible? 

I don't think it should matter if you went 3 and out and punted a kick to the point your rival had to start at the 5 yard line. I also don't understand why after a field goal, or touchdown, why your kick off team kicker cant kick the ball out of bounds as close to the end zone so that you, the receiving team has to start as far back as possible.

Punts and kickoffs are different things and treated differently.  There are simply different rules for each.

Punts - can only be recovered/advanced by the receiving team.  Can be kicked out of bounds.

Kickoffs - are LIVE BALLS, meaning either team can recover/advance the ball.  Kicking out of bounds is a penalty because the receiving team is expected to get an opportunity to return the ball.

---

In rugby, you can kick the ball to yourself. It’s a beautiful thing.

Boru

In a weird way you can in American football with the onside kick.  I've not seen it work all that well.  A short kick and your team recovers it so in essence you are attempting to kick it to yourself (or your team, as it were).  

It's a fascinating thing to watch (in a' this isn't going to go well kinda way') when watching young kids playing in rec leagues and junior high.

That's not really the same thing.  ALL kickoffs are live balls and recoverable by either team.  The punt is more closely related to the Rugby kick.  A punter could catch his own punt, but he can't advance it and of course it would mean the punt didn't go very far so it's not a good thing if/when it happens.