Does preference shock perturb equilibrium stochastic discount factor in the DSGE model

Dear Johannes,
In the paper of the PDF attachment, in equation (17) on page 1705
DSGE1.pdf (726.6 KB)
, the preference shock perturbs the equilibrium discount factor. I find most other papers use the terminology of ‘stochastic discount factor’ and there is the preference shock does Not influence stochastic discount factor. My question is does it mean the preference shock only influence equilibrium stochastic discount factor but Not stochastic discount factor?
Thank you very much and look forward to hearing from you.
Best regards,

I am not sure I understand the distinction here. The SDF usually is an equilibrium object.