Yep, and most modern systems let you enter the long address in decimal and program CV17 and CV18 for you... the days of manually calculating the CV17 and CV18 addresses is so long gone, I was not going to introduce the mechanics at first.
So to move forward a bit...
"what do we do with these 3 addresses?"
You tell the decoder to respond to the short or long address by setting a CV. It will always respond to the consist address if set.
You can tell the system, usually on a per throttle/cab basis to "call" or "select" a loco with long or short addresses. Some systems just use something special to eliminate the overlap, like entering 3 means short address 3, and entering 0003 means long address 3.
Consist addresses usually are entered like a short address.
So now, you, the operator can determine how to address a loco or consist, no matter how it is addresses.
But, when would you want to use short addresses when you see that they are limited to 1 to 127. In my opinion, unless you have some really old control system, never!
Electronics is so inexpensive today, compared to the cost invested in your locos that it's silly.
What I do is use long addressing, and use the loco number for the address. makes it simple. You basically have up to 4 digits when you do this.
By not using short addresses, I avoid most of the overlap danger, i.e. if I have loco 27, then it's long address is likewise 27...
The only overlap is consist addresses... I normally adopt a convention to take the first 2 digits of the lead loco in a consist as the consist address, but you can do it any way you want. Since the addresses are 1 to 127, picking a 2 digit number means all 2 digit addresses are available.
Also, it eliminates you using short addresses 1-9 for locos. This is normally a good idea, since the default short address of a decoder is usually 3.
As an aside, I normally never change the default short address of 3 and always use long addresses. If I must use the loco on some antiquated setup, then I switch back to short addressing and I know the loco short address is 3.
Whew, that was a lot, any questions or helpful comments?
Greg