Re: What is your art?
For me, Aikido is like a PhD level practice, done correctly. I focus on the development of Aiki when studying Aikido and not on the rote mechanics of Jiu Jistu these days. So, that is what I mean be done correctly. BJJ done correctly is a very good form and methodology to develop some very good jiu jitsu skills and at the advance level, BJJ can also encompass aiki as well.
If I were to start a brand new student out, I'd tell him to spend about 5 years doing BJJ before ever stepping into an Aikido dojo. Either BJJ or Judo actually, both a great arts for developing very good and essential grappling and jiu jitsu skills that are frankly not taught very well in most aikido dojos.
So if you ask me how they are related...it depends on your focus and perspective. Aikido practices can very greatly from dojo to dojo and student to student. I find the body work and structure you learn in BJJ to provide a solid structural frame work for understanding basic kinesiology and proprioceptive martial movements. Again, taught as a "advance practice" Aiki training can help further your Judo or BJJ practices.
Same goes for Baseball, Golf or any other sport. They just may not be as direct an application as two martial practices.