Difference between machine/processor/hardware-platform

In using the uname command the following three options gives me the same output:

ubuntu@ip-172:~/asm/asm$ uname -p
# x86_64
ubuntu@ip-172:~/asm/asm$ uname -i
# x86_64
ubuntu@ip-172:~/asm/asm$ uname -m
x86_64

Are the -m, -i, and -p options essentially the same thing, are what is the difference between them? From the man:

-m, --machine
-p, --processor print the processor type (non-portable)
-i, --hardware-platform print the hardware platform (non-portable)