Airplane tickets have both boarding time and departure time listed.
Things I walk up to momentarily before departure: every mode of transportation except planes. For trains and buses, the two times should be almost simultaneous (as anything else is just adding additional linger time)
Which varies in my experience. If there's an available window 5-10 minutes early, I've absolutely seen planes take it. And, of course, conversely delays are not infrequent. They presumably won't leave before boarding time (and don't think I've ever observed that) but I have seen boarding time be very close to door closed time. I've had connections that seemed pretty comfortable and I've ended up being pretty much the last person on the plane.
I once saw a plane leave before boarding time. Everyone was in the terminal already and bad weather was coming so the pilots rushed boarding to get in the air before the storm (well they tried: we spent 20 minutes on the taxiway waiting out the storm, but if they had been 1 minute faster they would have been able to get above the storm before it hit)
It is probably the anchor for everything else. The plane had scheduled a flight plan based on that departure time. Check in might close consistently X minutes before that, but sometimes not. I have been at an airport (pre covid) 3 hours early and only just made it on the plane due to airport chaos.
The reality is that transportation operations involve multiple events, each of which have a specific timing factor and variance.
There's arrival and departure (to the gate, platform, or quay) of the vehicle / vessel itself.
There's ticketing and check-in time, if those are required. Possibly security screening for air travel. And for aircraft, gate arrival time vs. wheels-down / wheels-up, where the latter includes taxi and takeoff queue time. Add to this the reliability or unreliability of actual travel times --- busses and shared-route transit must deal with traffic and delays, aircraft with weather and airport conjestion, ships with dock and pilot availability as well as weather factors, for example.
Schedules are written from several points of view --- the operator (when must vehicles be at specific points or departing from them), passengers, port or terminal operators, etc. Each has different needs. Learning how to interpret the published schedule to your own planning is key to effective use of such systems.
When the doors open, depending on traffic, they easily spend less than 20 seconds open before closing. I've run for a tube and dove in just in time _so_ many times now.
Is there anything with a departure time where you expect to be able to get on momentarily before departure?