When a shaped ski is put on edge, it will bend and describe an arc on snow, with a radius in direct relation to the ski's properties (sidecut, stiffness) and the situation at hand (speed, snow conditions) and of course, the skier's input (pressure, edge angle, fore/aft). If we need to get the ski to turn with a tighter radius, to make a shorter turn, one way is to oversteer the ski.
There are several ways to oversteer a ski, including:
If the ski is flatter on snow and the skier stays in the middle of the ski and does not do anything special, then the ski will make a pretty long turn, at a higher radius than the sidecut turn! If the ski is at a higher edge angle than the one it takes to engage, it will turn quicker, at a smaller radius than the sidecut turn.
When carving, the radius can be tightened generally by making the ski bend even more. When skidding, on the other hand (less edge angle) the skier will typically oversteer the ski, to get a shorter turn!
Pivoting is about the skier forcefully rotating the ski around its own axis (twisting the ski to point in a different direction) - these work when the skis are flat and stay relatively flat, at low edge angles.
Steering is "guiding" the ski around the turn, with the same effect of having the tails displace more and thus oversteer.
Managing the pressure fore/aft works by oversteering a part of the ski (the tails). So, being very far forward on the skis will unweight the tails and not allow them to engage, therefore cause them to step out and skid out. A similar situation occurs when the pressure is too far towards the tails and the tails are overloaded and effectively skidded to make the ski overturn - i.e. tail pushing.
To affect pressure fore and aft, the skier can move fore or aft, or leverage the skis or just mount the bindings more forward or aft on the skis etc. Most skis have the bindings mounted further back than the middle of the ski, so they have some "built-in" oversteering - whereby the tail is pressured more than the tips, just by standing on the ski!
The interplay between pressure and edge angles gives us a lot of other ways to oversteer the ski, from pushing the skis laterally while unweighted (redirection) to weighting an engaged ski.
Managing the pressure on/off basically means that we can control, to some extent, when and how much to pressure the ski. Note that it's incorrect to think that "more pressure bends the ski more". Pressure alone cannot bend a ski more (as the ski is supported by the snow), so standing on a ski edged at say 30 degrees, even if you double the weight on the ski, it can't bend any more! What happens is, if you increase the ski edge angle, then the centrifugal force required to stay in balance increases, so the resulting pressure increases, so the ski bends more - but is this a result of more edge angle or of increased pressure?
Changing the edge angle works by reducing the edge angle versus what it would take to engage the edge, so we allow skidding and over-turning, especially as the ski is unloaded, while by increasing the edge angle we make the ski engage and reduce skidding and over-turning. Increasing the edge angle, when you can (heh) will result in a ski that bends more, so a tighter arc.
The timing of pressure is more interesting and subtle and works by loading the ski when either not edged sufficiently or early, before it engages, to get it to point more into the turn - so that when it engages, it engages later in the arc. This is done at the top of the turn and in conjunction with the extension - so a more forceful lateral extension when the ski is unloaded and not edged enough would cause the ski to redirect.
This is the typical oversteering mechanism in racing and performance skiing, i.e. skiing at higher edge angles - where pivoting and steering don't work well (because the ski is tipped to a high edge angle early in the turn, too quickly for a rotation in the ski plane to have an effect).
In the typical racing scenario, the racer is flexed in transition and the skis don't spend enough time being flat on snow, for pivoting to be effective.
Racers switch edges quickly and go to high edge angles quickly.
Although above there was no redirection, it is typically done when the ski is unloaded, at the top of the turn (in left side in the example above) - see Stivot which is a related technique to control speed and turn shape on the steeps by skidding the top of the turn.
The general idea of good, "effective" skiing is to avoid big movements that disrupt balance, especially things like pushing the skis away from the body, twisting and pivoting the skis (rotating the skis with effort) etc. These introduce momentums which tend to disrupt balance and reduce control and precision (partly because they require us using some of the larger muscles of the body).
The concept of brushed carving describes a short turn made without any balance-disrupting inputs from the skier, where the tails still follow the tips in a round arc, as opposed to a Z turn.
Brushed carving is making short turns via "pure" turns using less edge angle than it would take the edge to engage fully. Basically, the skier makes a carved turn, but puts the skis at a smaller edge angle and not let them engage. The turn ends up more smeared and shorter radius than the corresponding carved turn.
Brushed carving is contrasted to pivoted turns, where the skier makes an active "pivoting" effort to take the skis off the edge and guide the skis around the turn.
The other mechanism to turn more than a given "sidecut turn", of importance in racing and performance skiing, is achieved by tightening the arc of a carved turn. This is managed by creating bigger edge angles, which help bend the skis more and reduce the radius of the turn - but this requires very good expert technique, much more than just tipping the skis a lot, see the High-C.
It is important to also note, despite all that talk about pressure, above, that it is much more beneficial to think of pressure as something that appears, as something that the mountain creates, as opposed to something that the skier creates. Read for instance, Resisting the pressure and Receiving pressure.
It is important to distinguish between so many oversteering mechanism also because some are more effective biomechanically and some are not.
In conclusion - don't focus on just pivoting - there are many mechanisms to get a ski to oversteer, some more disrupting to balance than others. Overall, the smoother we are, the better and the more we use the ski design as opposed to "effort", the better.