Ah. Okay, what you're seeing in the first waveform is, the voltage is fixed by transistor (pulling down), so the current varies due to dynamics. You see the armature bounce or whatever it is, and for whatever reason, it apparently bounces exactly twice. (Maybe this depends on what's in, or connected to, it? Maybe it varies from shot to shot?) At turn-off, there is no clamp diode* holding coil current, so current falls rapidly. In the third waveform, we see the reflection of this: voltage is allowed to freewheel quite high, and voltage varies due to dynamics. We see one bounce.
In the second waveform, voltage is fixed during both phases, and so the bounce is visible in the current flow, in both cases. Evidently, this time it only bounces once, even though the voltage, current and rate seem to be the same.
*It would be quite irresponsible to have no clamping whatsoever; what's normally done is, either a higher voltage TVS clamping the excess voltage to ground, at a voltage somewhat below the breakdown rating of the switch; or a protected switch, which turns on the switch a little bit if voltage goes too high -- serving the same purpose, clamping excess voltage to ground. As you can see, this only lasts a few ms, or fractions of a ms, it's not a huge amount of energy.
MOSFETs apparently wear due to breakdown, even though you'll find some rated for one-time or even repetitive avalanche. The current flow mechanism is fundamentally different between breakdown (Vgs off, Vds > Vds(max)) and conduction (Vgs > Vgs(th), Vds < Vds(max)). The latter is reliable in continuous operation (granted that thermal and stability limits are observed), the former is not.
The difference to the diode clamping method is, fall time is as fast as can be. This affects mechanical speed to some extent, which is most exaggerated on very small and fast actuators, like fuel injectors. Consider: if the armature only takes 5ms to travel, but it takes 10ms for the current to discharge, is it really going as fast as it can? Of course not. So, it can be a good idea to use a zener/TVS or the like.
It's also cheaper, when using protected switches which are also protected against current and temperature; so they use a lot of those in automotive applications. At least, I'm guessing that's what's in the ECU.
Tim