in the national football league, if a football player has the ball and
is running clear, then happens to stumble and fall and loses the ball,
is that a fumble or is he down by contact?

If there is no contact: a player with the ball can sit down, twirl
around, bounce the ball (careful not to bat the ball, that's
illegal!...whatever they want, that ball is live.  It is a fumble.

down by contact: Describes when a player with possession of the ball
is made to touch the ground (other than hands or feet) by a defensive
player; for example, if the ball-carrier slips and falls, he can get
up and continue, but if he was pushed by a defensive player, he is
said to be down by contact and the play is dead. This term is only
applicable to professional football; in college and high-school
football, the play ends when the player with possession goes down for
any reason. (source: wiki: http://en.wikipedia.org/wiki/First_down)




Here are some other cool things about fumbles:

 4. On a play from scrimmage, if an offensive player fumbles anywhere
on the field during fourth down, only the fumbling player is permitted
to recover and/or advance the ball. If any player fumbles after the
two-minute warning in a half, only the fumbling player is permitted to
recover and/or advance the ball. If recovered by any other offensive
player, the ball is dead at the spot of the fumble unless it is
recovered behind the spot of the fumble. In that case, the ball is
dead at the spot of recovery. Any defensive player may recover and/or
advance any fumble at any time. (source:
http://www.nfl.com/fans/rules/fumble)

Plain and simple rule. If someone touches him that makes him fall(knee
down) then he is down by contact. If nobody touches him and he just
randomly falls and loses the ball then its a fumble.