I see this question is more conceptual and applies to all kinds of semiconductor switches, not just BJT.
Yes, you want to switch fully on (to saturation, in BJT terms) to minimize the power loss and heating in the transistor, and provide as much of the power to the load.
If you want to use pulse-width modulated drive to control average power to the load, the idea is the same: always drive the transistor either fully on, or fully off, to minimize wasted power. You can't avoid a transition region where the transistor goes through the partially conducting mode (active region in BJT terms) - to reduce power dissipation, do that as quickly as possible.
However, in some cases, you want to drive the load with a nice, smooth voltage, not forcing it on/off alternatively. In this case you need to use the active region, with some sort of feedback. The downside is, power is wasted as heat in the transistor. Examples of this are linear voltage regulators and classical class A, B or AB audio amplifiers.
In the modern days, using transistors as switches (fully on / fully off) has become much more typical than driving them in partially conducting. Obvious example is digital logic; additionally, switch-mode power supplies have largely replaced linear power supplies. These circuits, however, tend to heavily use MOSFETs, not BJTs. With BJTs, you see partially conducting active region quite a lot, and will keep seeing it. Using BJTs as simple switches (100% on / 100% off) is becoming quite rare, to be fair.
The fact that transition to "fully on" depends on the load current is the same for MOSFETs, as well. You have the idea correctly; if you have just enough oomph driving the transistor to make it fully on at a load of 100mA, you need more oomph for it to be still fully on at a load of 200mA. For BJT, this oomph is base current; for MOSFET, this oomph is gate voltage.