Short Answer
Does the difference have to do with the restorative nature of the double inverters (buffer)?
Yes.
the difference between the two blocks is then a different in degree rather than a difference in kind?
In terms of function, yes, the transmission gate can be considered as being more analogue than the tri-state buffer, but in terms of implementation, they are quite different: basically, the tri-state buffer is a transmission gate with a buffer stage added.
Detailed Answer
The transmission gate can be thought of as a voltage-controlled resistor linking it input to its output. The resistance value is controlled by the voltage at its control node (its gate, connected to signal "e" in the figure you posted); when e is ON the resistance value is low; when e is OFF the resistance increases by several orders of magnitude (see example below). Sometimes signal e may be considered an analog value, in which case the resistance is a function of e, but most often we consider e to be a digital value, either on or off.
The tri-state buffer is identical to the transmission gate, but it has an extra block: the buffer (either inverting or non-inverting).
Transmission gate example: the venerable CD4016B.
Input to output resistance:
State = ON, R~ 1kΩ (Vdd=15V, Vcontrol=Vdd, Vin ~Vdd/2).
State = OFF, R~10MΩ (<1uA of current flows between input & output, for Vin ~10V, Vdd=15V, Vcontrol=0V).
Link:
CD4016 info at Digikey:
https://www.digikey.com.au/en/products/detail/texas-instruments/CD4016BM96/1690772