Okay. So this question was an eye opener for me. Before this i always thought that rugby and American football or NFL are the same. However, after this i read a bit about both the sports and tried to understand the difference between the two. I loved rugby before this but now i love NFL more… 
So the main differences between the two sports which might seem similar are:
Number of Players
In rugby there are 23 players, 15 on the field and 8 reserves. The starting 15, if they once leave the ground cannot come back on the field barring a serious injury or concussion or any other unavoidable emergency.
In NFL or American football a team is made up of three parts, defense offense and a third part which is comes under kicking scenarios. Defense and offense has 11 players each. The offense comes in action when the team has the ball whereas the defense comes in action when the opposition has the ball. The third team comes on to the field on situation such as kicking the ball for extra points or punt balls etc etc.
Time
The rugby is played in two halves of 40 minutes each whereas NFL is played in 4 halves of 15 mins each.
Tackling
In rugby in the Player who is carrying the ball has been tackled and is brought down to the ground but the defense or even offense passes the ball then the game continues whereas in NFL if the player carrying the ball is brought down to the ground the game stops. And the offensive team or the defensive team gets one more chance.
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Ground Length
In rugby the ground is of 100 metres whereas in rugby the ground is of 100 yards where one yard is about 0.91 metres. Nfl ground is divided into 10 equal parts of 10 yards each. The team that is the offensive team or is attacking will get 4 chances to clear one 10 yard parts in four parts, if they manage it it’s called a touchdown and they get another 4 chances to clear the next part whereas if they fail the opposite team gets the offensive and the team attacking defends and the opposite team will get 4 chances to clear one part. This cycle continues.
