I would only use the term "moonlighting" if it was a job which isn't declared to the tax office ( so be careful to whom you say this! It wouldn't look good on an official form... a visa application for instance) Otherwise, I'd say I'm a "xxx" , and I also work part time as "xxx".

If you work Mon - Fri 9AM to 5PM this is called a day job. Moonlighting usually meant something you do part-time, after work, possibly at night (by moonlight)...but now it can mean anything you're doing through self-employment, or yes, a part-time or casual job. You don't need to use "external" with it... Some possibilities: I have a day job and I moonlight a few nights a week. I have a full-time gig but I also work for myself outside regular work. I work full-time as a (whatever) but I've been moonlighting as a (other job) for a few months. I am a full-time (position) to pay the bills but I work part-time as a (whatever) because that's what I love. I am moonlighting as a (whatever) to make extra money.

"Moonlighting" is used by itself. ---- "I am a teacher. I'm also moonlighting as a an actor/waiter/etc.."

part time job if it is part time, a secondary job if it is full time job