There is no significant difference in meaning between form 1 and form 2 here. I would think of 1 as a shortened, informal version of 2. The version 3 suggested by FumbleFingers:
(3) So if my cat were to tear up the curtains, I would have to pay..
would be the most formally correct form, in my view, but there is still no change in meaning, and a fluent speaker would easily understand any of these forms, and might use any.
I would note that "numbered" conditional types, as used by many ESL teachers, are not normally taught to or used by native speakers, and many will not understand what each number means. Moreover, the numbered types do not include all valid conditional forms, only the most common versions. I advise against using such numbers for conditional types, except when speaking with people trained in ESL teaching.
There is no implication that any of these means the speaker is treating the possibility more seriously, or showing more concern, than any other version. Tone of voice or manner might convey such and implication, or additional context might suggest such an implication.