With the DC breakers your thinking that a faster trip time is from higher current is correct to a point, as you get above the instantaneous trip current ( depends on the breaker and how hot it is) the trip time drops, as there is more energy put into the trip coil to generate a magnetic field acting against the inductance of the coil.
Ac trip you can see the trip time is dependant on energy, but also the trip is shown by the small variation of current and voltage, followed by the tail off to a zero current as the breaker points separate and the current drops as the arc between the contacts dissipates power. As the mains peak ( irrespective of whether it is positive or negative, the power in each case with a resistive load is going to make a positive power flow into the load) shows there is a lot of energy put into the coil to build up a field, and this is shown by the short time betwen closing and the small wiggle as the contacts start to trip, followed by the arc dumping power. At the switch on into a close to zero point the current will build up slowly, and the breaker will trip slower just because the field is building up slower.
Note that in all the cases the breaker had started to trip within a single half cycle of the incoming mains, irrespective of when the overload occurs. With a lower load then you will be depending on the thermal trip, which can take a long time ( up to hours for only a small overload) to trip the breaker. The current tail is the main danger of using a breaker rated for AC on DC, as the arc will not extinguish properly as there is no zero crossing points to help by reducing power to zero, which cools the arc channel so that eventually it no longer is ionised.
A high enough voltage ( with a typical residential AC breaker) of around 60VDC ( 5 car batteries in series) and a low enough resistance load ( 30A of resistor that can handle the current for a while) and try to break that with an AC breaker will result in it arcing continuously, and not breaking the current path at all, which will burn the breaker to char in a few seconds. That is why you typically see breakers have a rating of 400VAC or 28VDC, just from that arcing.
