[Goose]

I'm not clear on this rule. In the Kentucky-Ole Miss game, the Kentucky player fumbles around the 2-yard line, but it is caught mid-air by another Kentucky player around the 2 and he steps and falls forward for the TD. What is the difference?

In the Kentucky-Ole Miss game it was first down, not fourth down. The college rule is that on downs first through third anybody on either team can advance a fumble. On fourth down the rules are different. The rule is:
"When on fourth down, before a change of team possession, a Team A fumble is caught or recovered in advance of the fumble by a Team A player other than the fumbler, the ball is dead and returned to the spot of the fumble. If the fumble is recovered behind the spot of the fumble by a Team A player other than the Team A fumbler, the ball is dead at that spot."

This rule is necessary because if you fail to reach the line to gain before being tackled it would in almost all cases make sense to just "fumble" the ball forward when you are hit. You may get lucky and a teammate recovers for a first down. If the defense recovers they are (most probably) in no better position than they would be for a turnover on downs (and quite possibly a worse one). This rule prevents doing it.

[Goose]

I'm not clear on this rule. In the Kentucky-Ole Miss game, the Kentucky player fumbles around the 2-yard line, but it is caught mid-air by another Kentucky player around the 2 and he steps and falls forward for the TD. What is the difference?

In the Kentucky-Ole Miss game it was first down, not fourth down. The college rule is that on downs first through third anybody on either team can advance a fumble. On fourth down the rules are different. The rule is:
"When on fourth down, before a change of team possession, a Team A fumble is caught or recovered in advance of the fumble by a Team A player other than the fumbler, the ball is dead and returned to the spot of the fumble. If the fumble is recovered behind the spot of the fumble by a Team A player other than the Team A fumbler, the ball is dead at that spot."

This rule is necessary because if you fail to reach the line to gain before being tackled it would in almost all cases make sense to just "fumble" the ball forward when you are hit. You may get lucky and a teammate recovers for a first down. If the defense recovers they are (most probably) in no better position than they would be for a turnover on downs (and quite possibly a worse one). This rule prevents doing it.