A bouncer is a short-pitched delivery that rises at the batter. A beamer is a high full toss that reaches the batter without pitching. Cricket treats them differently because one has bounced and the other has not, but both can become no-balls when they create an unfair or unsafe delivery.
A bouncer is not automatically illegal. It is a normal part of fast bowling when it pitches short and rises toward the batter, provided it stays within the Laws and any competition playing conditions.
A beamer is different. It is a delivery that does not pitch before reaching the batter and is high enough to be dangerous or unfair. Under the Laws, the key height line for a non-pitching delivery is waist height, judged against the striker standing upright at the popping crease.
The clearest height rule is head height. If a delivery pitches and then passes, or would have passed, over head height of the striker standing upright at the popping crease, the umpire calls and signals no-ball.
That judgment is not based only on where the batter's head actually was after ducking, swaying, jumping, or playing a shot. The umpire is judging the ball against an upright striker at the popping crease, which keeps the decision tied to the delivery rather than to the batter's reaction.
A short-pitched delivery can also be dangerous even if it is not simply called under the head-height rule. The bowler's-end umpire considers the speed, length, height, and direction of the delivery, and the skill of the striker, when deciding whether short-pitched bowling is likely to inflict physical injury.
Protective equipment does not excuse dangerous bowling. The umpire makes the safety judgment as if the batter's helmet, padding, and other protection did not remove the risk.
Short-pitched bowling can become unfair through repetition. Under the Laws, the umpire may treat short-pitched deliveries as unfair if they repeatedly pass above head height of the striker standing upright at the crease.
Many professional and limited-overs competitions add their own bouncer limits or guidance. Those limits are playing-condition rules, so they can differ by format, age group, league, and event. Do not assume that a Test match, one-day match, T20 match, or local competition uses the same per-over limit.
For a delivery that has not pitched, the key Law is the waist-height rule. If it passes, or would have passed, above waist height of the striker standing upright at the popping crease, it is unfair and the umpire calls no-ball.
This is why a full toss at knee, thigh, or ordinary hitting height can be legal, while a full toss that rises above the waist can be illegal even if it was accidental. The ball does not need to hit the batter for the no-ball to be called.
A high full toss above waist height is always a no-ball under the Law. It becomes a dangerous non-pitching delivery if the bowler's-end umpire considers that it creates a risk of injury, looking at the speed, height, direction, the striker's skill, and whether similar deliveries are being repeated.
If the umpire considers the beamer deliberate, the bowler is not given the ordinary warning first. The umpire calls no-ball and, when the ball is dead, has the bowler suspended from bowling for the rest of that innings.
For dangerous or unfair short-pitched bowling, the first such decision brings a first and final warning to that bowler for the innings. A further such delivery by the same bowler in that innings leads to immediate suspension from bowling for the rest of the innings.
For dangerous non-pitching deliveries, the warning sequence is separate. The first dangerous beamer brings a first and final warning for that bowler in the innings. A further dangerous beamer by that bowler leads to suspension. A deliberate beamer skips the warning and leads to immediate suspension.
A no-ball adds one run to the batting side and does not count as one ball of the over. The ball is not automatically dead just because no-ball has been called, so batters can still run and a boundary can still be scored unless another Law makes the ball dead.
Dismissals are also restricted. From a no-ball, a batter cannot be out in most ordinary ways, but can still be out hit the ball twice, obstructing the field, or run out. In limited-overs cricket, a no-ball may also trigger a free hit under the relevant playing conditions.