I can see why you're a little confused about this, as Moneygram's website doesn't seem to make this information very clear. I had trouble finding it, anyway...
Don't worry, though, as the members of the Blurtit community have - as always - come to the rescue! They suggest that the best way to check the status of a Moneygram is by phoning 1-800-542-3590, and quoting the ID number that you have been given.
I gather that this is a free 24-hour tracking number, which is useful as it is apparently not possible to track Moneygrams online.
You will need to enter the ID number once you are prompted to do so, and you will also need to know the exact amount of the money order that you wish to check the status of.
Alternatively, I understand that you can also check whether your money is available by calling (800) 666 3947. You will need to use a touch-tone telephone to do this.
You will then be asked to say whether you wish to use the sender's phone number, or the reference number, to check the status of your payment.
You should then say either the sender's phone number, as mentioned above, or the reference number - at which point the system should advise you whether your money is ready for collection.
If it is, you can check the different collection outlets available by going to the Moneygram website, here - or by phoning the customer service number given at the beginning of this answer.
Don't forget that you will need to take some form of picture ID (identification) with you, when you go to collect your money.
For further details of what to do when using Moneygram, follow this link, to read a discussion about the subject on Blurtit.