So, sometimes when I send a text, once it is sent, a check mark appears. Other times, when I send a text, a check mark with a little "D" appears. What does that mean?
I only get the C/mark + D when I'm sending it to another Verizon user
Indeed. You will only get the D when sending to other Verizon users. Not sure if this goes for other carriers as well - kind of a drag that you can't see if messages are delivered to people on other carriers as well.