Is there a distinction between Tapped-Delay-Line Filters and the more general FIR (Finite Impulse Response) filters. From what I understand the Tapped-Delay-Line is a type of FIR filter since it's impulse response settles to zero in a finite duration...but I'm having trouble determining what might make these two things separate in the world of DSP.
A tapped-delay-line is really a methodology or implementation. An FIR filter is a more general description of a purely feedforward digital network.
While your impulse response is finite (no feedback components) you can consider the tapped-delay-line filter to be a particular FIR filter whose coefficients are non-zero at tap positions and zero otherwise.
Should you introduce feedback components, I think you could still describe the system as a tapped-delay line filter, but it would cease to be an FIR filter at this point and become an IIR filter.
A delay line just delays the signal injected to its input. The amount of delay can be integer or non-integer (fractional). If the delay is integer, then it can be implemented by buffer (memory) elements only. However, fractional delays imply some sort of interpolation between two known integer points. Hence, they require an extra level of filtering.
A tap, implies the signal is extracted from the delay line at a certain point.
By definition, you can see tapped-delay line is just a building block. Now you may use it for many different purposes. A few examples:
A causal FIR filter can be represented by a tapped delay line whose delay elements have unit (integer) values, and the delay line is tapped at all delays. The output is just a weighted sum of the tap values (a zero weight is also possible). Note that the FIR filter should be causal.
The numerator and denominator of a causal IIR filter (similar to causal FIR).
More generally, direct forms of digital filters make use of the tapped-delay lines for implementation of ordinary difference equations that describe LTI systems.
Other applications for signal modeling in a specific domain(e.g. acoustic echo modeling, etc.).
So we can see tapped delay line is a building block that can be applied to model and implement digital signals and systems.