ataylor32 wrote:It is my understand that service missions are not the same as full time missions. Should I use "Missionary - Full Time" even though that isn't technically accurate or should I create a custom position or should I do something else?
It's up to your ward to decide. The callings you enter will show up on the Directory on LDS.org in the Leadership section (but service missionaries will not show up in the Missionary section, regardless of what you enter in MLS). If you want to distinguish between the proselyting and service missionaries, you could certainly create a custom calling for the service missionaries.
Questions that can benefit the larger community should be asked in a public forum, not a private message.