Hello,
To call your friend’s US mobile phone (assuming your friend has an international plan and therefore is able to use the phone abroad) you do not need to add any international codes to the US number – just pretend that your friend is still in the US and dial the number accordingly.
The Philippines number showing on your caller ID is a mobile phone as well. My guess is that your friend also has a local cell phone (or maybe he’s replaced the US SIM card with a local SIM). To call the Philippines cell add 011 to the number: 011 63 and so on.
The difference between the two situations in terms of calling costs incurred is that, in the first situation your friend would likely pay a high roaming rate to receive your calls while receiving calls on the Philippines cell is free (although this time you’d pay to dial internationally).