What is the difference between write and flash
Write and flash are not comparable. The former is a "action", but the latter is a "noun".

write to flash/ram: Write something (such as your binary file, but can also be others) to the flash or the RAM, this is so called "programming the flash/RAM" or simply "programming".

flash from binary file: Means write your binary file (such as your binary program) to the flash memory. The difference with the first is this designate the source ----- a file.

read from flash/ram: Read data from the flash/RAM.

save flash to binary file: Has similar meaning, but it designate the target ---- a file.