A0/D14 - Use A0 when you want to do analogRead.
Use D14 when you want to do digitalRead or digitalWrite.
If you look at pins_arduino.h, that tells the code the mapping from PortD bit 3, to D3 as an example.
The physical package pin # is different between surface mount and through hole package, the software does not know which package it is running on. Purchased boards are labelled with D3 so you don't need to look that up every time. If making your own board, or running a standalone chip, you have to be aware of that.
There are pictures around showing the physical pin mapping.