As
russellhltn posted there are four units identified for a missionary. You can check MORS to see if your unit is one of those four. If so you should see a link, "Other Units" to the right side of the page that identifies those units. The unit identified as the membership unit will show the serving missionary on the LDS.org Directory as a serving missionary. I believe those same missionaries will be also be displayed in LCR > Organizations > Full-Time Missionaries and in LDS Tools > Missionary > Serving. The unit with the missionary's record will be the unit identified as the "membership unit".
There is a tool tip link, "(List Incorrect?)", in the LDS.org Directory just below the Serving Missionaries title that provides this tip:
List Incorrect?
You may notice missionaries missing, or who do not belong in your unit, in the Serving Missionaries list. This is common if the family has changed units since the missionary was called. You can work with your clerk to help the Missionary Department correct this. Your clerk can contact the Missionary Department at 801-240-2222.