Don't listen to the announcers. Just because a pitch is "tipped foul" doesn't mean it's a Foul Tip. A Foul Tip is specifically defined in Rule 2.00 of the Official Baseball Rules:
A FOUL TIP is a batted ball that goes sharp and direct from the bat to the catcher’s hands and is legally caught. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball is in play. It is not a catch if it is a rebound, unless the ball has first touched the catcher’s glove or hand.
1. A batted ball;
2. That first strikes the catcher’s hand or glove;
3. That is caught (by the catcher).
The most common occurrence of a Foul Tip is when the batter nicks a pitch, and the ball goes directly into the catcher’s glove, and is caught for a strike. Here is a video example of a batter striking out on a foul tip.
The status of the ball for a Foul Tip never changes. A Foul Tip remains a live ball, is not dead, and is not delayed dead. Here is a video example of a foul tip followed by a throw out a second. The Comment to Rule 7.08(e) states:
Runners need not “tag up” on a foul tip. They may steal on a foul tip. If a so-called tip is not caught, it becomes an ordinary foul. Runners then return to their bases.
A Foul Tip must go sharp and direct from the bat to the catcher’s glove or bare hand. Here is a video example of a pitched ball that is nicked, but that does not go sharp and direct to the catcher’s hands. This is a Foul Ball that is caught for an out, and is not a Foul Tip caught for a strike.
A Foul Tip must touch the catcher's hand or glove first. Here is a video example of a pitched ball that is nicked. The ball travels sharp and direct to the catcher’s hands, but then ricochets into the air. The catcher then catches the ball before it touches the ground. The batter in this video is out because it is strike three, not because it is a caught foul ball. Had the not touched the catcher's glove (or hand) first, this ball would be a foul ball and immediately dead since it touched the catcher's body.
The PBUC MLBUM interpretations state that only the catcher may catch a foul tip. This interpretation is the same for NFHS and NCAA.
A Foul Tip must be legally caught. The Comment to Rule 6.05(b) states:
“Legally caught” means in the catcher’s glove before the ball touches the ground. It is not legal if the ball lodges in his clothing or paraphernalia; or if it touches the umpire and is caught by the catcher on the rebound.
Furthermore, the Comment to Rule 5.09(g) states:
If a foul tip hits the umpire and is caught by a fielder on the rebound, the ball is “dead” and the batsman cannot be called out. The same shall apply where such foul tip lodges in the umpire’s mask or other paraphernalia.
In this video example a pitched ball is nicked, goes sharp and direct to the catcher’s glove, but the catcher does not catch the ball. The ball is stuck in the catcher’s mask and cannot be caught according to the Comment to Rule 6.05(b). Therefore, this is a Foul Ball.
The Comment to Rule 6.05(b) also states:
If a foul tip first strikes the catcher’s glove and then goes on through and is caught by both hands against his body or protector, before the ball touches the ground, it is a strike, and if third strike, batter is out. If smothered against his body or protector, it is a catch provided the ball struck the catcher’s glove or hand first.
In this video example the pitched ball is nicked, hits the catcher’s glove, then passes through the catcher’s chest protector. Is this a ball that can be legally caught for a strike? Sometimes it is difficult to apply general rules to unique situations.
A nicked pitch cannot be caught for a Foul Tip if it first hits the ground. Sometimes it is very difficult to know if the ball hits the ground first, as in this video. A nicked pitch that hits the ground first is a Foul Ball.