Wet vent vs. soil stack?

I'm confused between the two subject line terms. I have a kitchen sink / dishwasher combo that drains into a 2" drain and has a 2" vent. I want to add a bar sink to drain into the 2" vent on the floor above the kitchen. There won't be an offset. Firstly, can I do this?

It seems from my code-check book that this can be considered a soil stack which appears to be allowed, or a wet vent, which appears not to be allowed - because the fixtures are on different floors. What is the difference between the two? Thanks!
Hazel

A soil stack is a vertical line of piping which conveys human waste, toilet and urinal stuff.

What you describe would be a wet vent. It is only allowed on the same branch interval, or story.

You will either have to add additional vents to your lower floor fixtures, which extend above your new sink sink, and tieing back into the existing vent.

Or, add a new waste line for your new sink and tie it in below the connection of your existing sink/fixtures. Your vent for the bar sink would tie into the vent stack from the kitchen.

vent

Your code book does not allow it, but the new UPC book might allow it as a "Philadelphia single stack" system, if an engineer, or your local inspector, approved it.