Being new to electrical engineering, I'm wondering why the TP4056 IC is called a "linear li-ion battery charger" (emphasis on linear). Is it because the TP4056 is designed to work with a constant voltage/current input? Or is it linear as in "linear power supply vs switching power supply"?
The TP4056 uses a pass transistor to regulate the charging voltage / current to the battery.
That pass transistor is controlled in a linear way, meaning a gradual on/off control. So the pass transistor can be fully on, fully off or any state in between (having a certain resistance).
A different type of regulator is the switched regulator where the pass transistor is switched so it can be on or it can be off. There is no state in between (like a high resistance state).
Or is it linear as in "linear power supply vs switching power supply"?
Yes it is.
It is linear as in linear power supply. It works by using a pass element, whose resistance is modulated so either constant current or constant voltage is supplied to the battery, charging it correctly.
Update: A pass element in a linear regulator is some form of a transistor, which is operated in its "linear"/"ohmic" region, so it is neither fully conducting ("on"), nor fully off. The magic is in the biasing circuit (the rest of the linear regulator) which provides suitable voltage or current to the gate or base terminal of the transistor, so the required amount of current is passed from input to output.