Is India sending up an astronaut
Yes. Shubhanshu Shukla will take part in an actual mission.
or is this person a passenger on a spacecraft like was the case with Katy Perry
Kate Perry was a tourist: she just paid big bucks to go have some fun at low G in a capsule.
What is an astronaut? I envisioned the term to mean the...
Nobody cares what you personally envion. (Just as you wouldn't care if I personally decided to envions you as a "Zorglub").
Check instead the first paragrph at Wikipedia:
An astronaut [...] is a person trained, equipped, and deployed by a human spaceflight program to serve as a commander or crew member of a spacecraft. Although generally reserved for professional space travelers, the term is sometimes applied to anyone who travels into space, including scientists, politicians, journalists, and space tourists.
So most of the time it's used for professionals taking part in amission.
And from the summary above:
They will conduct 60 scientific studies, including microgravity research, earth observation, and life, biological and material sciences experiments.
They are not tourist who merely paid to go frolicking in weightlessness.
They are trained professionnals sent on a mission that includes working on experiments and other scientific goals.
person had some control over the spacecraft, or at least some task vital to the function of that spacecraft,
Crew are part of the astronauts.
In its most widespread use the term "astronaut" isn't restricted to a specific task like controlling the spacecraft (that would be a "pilot") and do pay attention that a lot of spacecraft across the history of space exploration have been significantly computer-controlled or on purely passive trajectory with very little piloting actually involved.
But for anyone of the trained professionals sent on a mission. If you want to find a seafaring equivalent, that would be an "explorer" or indeed as you hint "scientist".
There's no equivalent of "sailor" currently in space as, due to high cost to orbit, etc. to make the most efficient use of the personnel sent up there, they are all trained to perform multiple scientific goals of the mission.
So you can clearly build a two column table with people like Neil Armstrong, Valentina Vladimirovna Tereshkova, or today's Shubhanshu Shukla on one side, and Kate Perry on the other.
Did they train professionally? One category did, the other merely passed a medical exam to make sure she doesn't accidentally die.
Did they get deployed on a mission? One category was, the other merely went up there for fun.
Were they either commander or crew? One category has membre which held various posts, the other was up there just for fun.
Another way to look at the difference is the same as between work travel and holidays.
Where I'm having trouble is calling people an "astronaut" because they took a ride above the Karman line, we've seen dogs, cats, and monkeys do that.
Ignoring the obvious attempts at dog whistling,
for fuck's sake, even Richard Gariott managed to have actual mission goals to accomplish (even if a lot of them were more in the field of public communication and raising awareness).
The only different between Richard Garriott is that his mission was mostly self-funded whereas most of the usual astronauts tend to be deployed on a mission by public agencies.
Kate Perry just paid to go have fun.