@Janey *****
I believe you are confusing TWO completely different things.
One is registering a marriage here in thailand <- meaning GETTING married
When you do that you need the affirmation of freedom to marry from your consulate here, you need it translated to thai, certified by the MFA and then you can go to the local Amphur and register your marriage (get married), and when that happens you get a Kor Ror 2 and a Kor Ror 3 (one is a rose borders suitable for framing document and the other lists you twos names and the date you got married.
The other is registering the fact that a thai was married overseas:
For that you already married your thai spouse in another country and all you're doing is getting the marriage from abroad listed in the registry of marriages (you're not getting married again ;) ) and when you do that you just get a Kor Ror 22