Bootstrapping, in both usages, means the arrangement of TWO nodes of the circuit that are coupled in such a way that one (controlled) node will closely follow the (controller) node.
If an emitter-follower uses the emitter output voltage to drive the collector voltage, then the Cob is removed from the Cin computation. This requires a large resistor in the collector to VDD, otherwise the emitter would not be able to move the collector voltage. A bipolar with Cob of 5pF, and a bootstrap cap from emitter to collector of only 5pF, will not optimally minimize the input capacitance; notice this is positive feedback, and some configurations of this are called "oscillators".
Another use is in high_side switching, using N-Channel FETs; a special capacitor Cboot must be charged up, and then charge is stolen from Cboot to control the Cgate of the FET during each switching cycle.
Also, the standard OpAmp non_inverting gain configuration is "bootstrapping" in that differential input capacitance is largely ignorable, as is differential input current. Thus the primary Rin (aka Zin) becomes the common_mode behavior. Note the Miller Multiplication (by non_cascoded input diffpairs) remains a problem; and during slewing, there is no Miller Multiplication, making the Cin become highly NON_LINEAR and upsetting the settling behavior.
Please read the comments by "jonk" and examine his links.