What a guy calls his unofficial girlfriend. It is derived from comparing the situation to an engagement, which is much like an unofficial marriage. In this case, the two people are not officially boyfriend/girlfriend, but they both know they will be in the near future, much like how the fiance and fiancee know that they will soon become husband/wife.
I will be taking my girlfriancee out on our first date next month.
Pajama casual is a term used when working from home and preparing for a video conference. All business above the waist and your pajama pants down below.