Ok, I feel pretty stupid now, especially because I browsed through that FAQ page. Thank you for your quick reply and patience with people like me 
So it seems to me that FOP assumes that an extension is always connected to one device, am I right?
But I could connect several devices to one extension. How does FOP handle this? (I browsed the FAQ again before asking this question).
We are currently in the proces of setting up or Asterisk server. I defined a few SIP phone devices and extensions, and I wanted to take a look at FOP2. We use the MAC adres to define the name of the device, or a string in case of a softphone.
I thought I'd take a look with a small config.. I only defined one extension, and my two trunks.. I don't have voicemails or queues setup yet, so I thought I'd comment that out.
[SIP/spRoland]
type=extension
extension=337
context=stumpel-zwaag
label=Roland
;mailbox=620@default
;extenvoicemail=*620@from-internal
;external=5551234@from-internal
;privacy=clid
;queuechannel=Local/620@from-queue/n|Penalty=1|MemberName=Nicolas|StateInterface=SIP/620
Now when I go to the webclient of FOP, I do see the button for extension 337, but I don't see the action buttons in the toolbar. I cannot dial, or do anything else.
I was also wondering: do these extensions in sop2.cfg (user=622:1234 for example) need to match the sip.conf in asterisk?
Am I missing something in my Asterisk config files?