I personally found these two biases extremely hard to distinguish, or at least in many situations I can explain with either bias.
I understand these two are from two different categories (cognitive errors and emontional bias). Accoring to Schweser, Conservatism bias occurs when “market participatns rationally form an initial view but fail to change that view as new info becomes available”. Status quo bias is “when comfort with the existing situation leads to an unwillingness to make changes”. It also makes sense to me to say status quo bias occurs because the unwillingnesss to make change is due to the fact that “market participatns rationally form an initial view but fail to change that view as new info becomes available” (i.e. conservatism bias).
Conservatism is a cognitive error: essentially, when new information arrives that contradicts the old infomation on which the decision was based, the person perceives the new information as a surprise or anomaly, rather than an indication that conditions have changed.