A Zip Code is just a numerical means of identifying the post office which handles all your incoming mail for you. In this case, 21236 is the post office located on Mercantile Rd. across the street from White Marsh Mall.
That post office services a wide area so you could see mail addressed to Perry Hall, MD 21236, Baltimore, MD 21236, Nottingham, MD 21236, etc... The name of the city doesn't matter. The Zip Code will get it to that post office and then that post office will deliver it to you based on your street address, but ONLY if your street is in their service area.
If you have a PO Box in at the White Marsh Post Office, "White Marsh, MD" is what's correct for the your mail. But again, as long as they use the 21162 Zip Code, that's all that really matters. Writing "Baltimore, MD" won't make a bit of difference on how fast it gets there.
The story I heard was that the Nottingham Post Office is a distribution center for all mail coming into and going out of the area. If that's true, then that means a piece of mail going to White Marsh would go through Nottingham before being delivered to the White Marsh Post Office for final delivery. And vice-versa, if you mail something at the White Marsh PO, it will go through Nottingham first. It's probably quicker to mail something from Nottingham, but whether it's quicker to receive is all up to timing of the trucks (unless you have a PO Box).
Here's a website that will show you Zip Code areas:
The Most Accurate Free USPS Zip Code Map Anywhere!