Does this master's course of study sound particularly like aerospace engineering?

(Cross-posted in Grad School forum)
I am almost halfway to my (course-based) master’s degree in an online course of study, and I am in my mid-30s. My courses include 4 classes related to fluids and thermodynamics, 2 FEA courses, and 4 courses on product design, such as design for manufacture or concurrent engineering. I started out thinking I would get a degree in aerospace engineering with a focus on propulsion, as it would be an application of the thermodynamics and fluids that interest me, but I have since found out that most propulsion-specific courses are only offered on-campus in another state. This course plan will satisfy the requirements for a MS in either aerospace engineering or mechanical engineering, as my school has a combined department for the two. Regardless of what the degree is called, these courses are a good fit to my experience, interest, and career goals.
I am wrestling now with whether there is enough in my 10 courses to make it particularly aerospace, rather than only mechanical. I worry that an employer would look at my degree, look at what I studied, and think there is a disconnect or that I don’t know the difference between the two. I liked the sound of a degree in aerospace engineering, but feels harder now to defend calling it that, now that propulsion is not in the picture. I am wondering whether to trade the “prestige” of an aerospace degree for the clarity of calling it a mechanical engineering degree. I will take the same courses, but I am trying to figure out which degree will help most in getting future job opportunities.
So to sum up, does a course of study with 4 fluids and thermo courses, 2 FEA courses, and 4 product design courses sound like aerospace engineering (MSAE), or does it sound like it should be mechanical engineering (MSME) instead?

Most job postings are looking for specific skills and openly sat they accept multiple degree titles. Personally, I think it’s more about your courses and experience than degree title. I also don’t think there’s more prestige in an AE degree than a ME degree to hiring engineers. @HPuck35 worked in aerospace his whole career and hired many engineers. He’s better positioned to answer. His degree was in Civil BTW.

I never cared what the title of the degree was. I was interested in what knowledge you had and whether it matched the job I was offering. I was also looking for team players as the job always involved working as a team.

Most of those courses are pretty standard, but the content of those product design courses will matter. They’re likely helpful for jobs that are related but won’t count for much if your goal is, say, a job more rooted in analysis, IMO.