Correct transfer function with 1st order IIR filter

Question

What diffreneces it makes in magnitude and/or phase response when using

$$H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}}$$ by adding $b_2=0$, $a_2=0$

instead of

$$H(z) = \frac{b_0 + b_1z^{-1}}{a_0 + a_1z^{-1}}$$

for 1st order filter?

All software I'm using for to build VST plug-ins (SynthEdit, FlowStone, etc.) implements a biquad (BLT) module for coefficient input and now it looks like I can't get 90° phase response with a filter designed using Octave (by Octave plot phase is 90°).

EDIT: Ok, digged the web a bit more and found these three (1 2 3) articles published at analog.com. Is the situation same with one pole allpass filter vs biquad allpass filter (what are the phase responses for these?)?

Answer 1

If the formula becomes the same, the response becomes the same – there's no difference to be expected.