So my brother and i get a birthday card for my mother the day before here birthday. He posts his in a letterbox first thing in the morning 1st class. I put mine in the same letterbox but at the end of the day (but before last collection). Is his card more likely to get to our mother the next day? Or are all the letters collected just dumped somewhere until last collection at which point the letters are sorted?
From personal experience, i can say that i’ve had a letter delivered across town on the same day - I mailed it in the morning, and it was delivered the same day in the afternoon. I can pretty much guarantee that wouldn’t have happened if I mailed it late in the day.
It also depends on how you address them. Typed addresses, or even better, addresses with the postal barcode included, can be machine-read and handled automatically. Very neat hand-printed writing can sometimes be machine-read, and less neat handwriting has to be processed by humans, which slows it down. Likewise, including the full 9-digit ZIP code speeds things up.
It will vary from city to city. In the small town where I delivered mail, letters posted at the office went out to the plant at 3:30 PM, before the city carriers returned from the street. Any mail we brought in left at 5:30 so, depending on many mysterious factors (lol) one mailed at the office could get there earlier.
As for a letter being delivered across town the same day, it’s possible that it was on the same carrier’s route, he or she recognized the name, cancelled the stamp by lining through it and delivered it. Carrier routes often end up quite a way from their starting point. Generally speaking, carriers leave the office with all the mail they will deliver that day.