Tapped Delay Line Filter Distinction
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.