Welcome to iPhone Forums!
When you send an SMS, the first status you'll get is "Delivered", then it will be "Read", as soon as the one who received the message has read it - a different order than the one you described. You don't have an influence on the status, it happens on it's own, afaik. That's why I'm wondering why it was different in your case.
My guess is that the recipient changed one of his settings after reading your message. If he or she owns an iPhone, this can be changed in Settings - Messages - Send Read Receipts. When it's enabled, you'll get "Read", as soon as the message has been read. If it's disabled, you won't get this status.
Hope that helps.