What we're now describing is more or less the power and torque curve as you rightly mentioned. My worry here is that we're kind of categorizing all internal combustion engines as having the same kind of power/torque curves when in fact a lot of internal combustion engines are very different from each other.

Some engines are capable of delivering 100% of torque the second (within a couple 100ms) of hitting the throttle. To name a couple:

1. The Mercedes M278 twin-turbo V8 makes 700NM of torque between 1,800 and 3,500RPM. In other words, 700NM of torque is available from little above idle.

2. BMW B58 single-scroll turbo i6 makes 500NM between 1,600 and 4,500RPM.

Other turbo charged engines, such as those in supercars, have different kind of turbos turned for a more linear torque and power curve to better replicate their N/A predecessors, such as the McLaren M838TE which makes 620NM between 5,500 and 6,500RPM.

Lots of different engines out there with all kinds of different characteristics and power/torque curves.