A check box will only display the values in its value list. If you change the field to be type 'Edit box' then you will see that it has (probably) imported all the values you expect. The field name isn't relevant, nor the name of the value list - it is the contents of the value list that is important. The new database must have defined in its value list all 6 potential values.
I'm not sure if you are also expecting the value list themselves to impoprt - they won't. You will have to change it manually, if it is defined as Custom Values.
How did you set your import settings.
Did you check the box for "Add remaining Data's as new records"?
EDIT: I think Sorbsbuster might have pointed out the most likely problem.
Thank you. I actually made a stupid mistake. The value in each database were the same except I added an "s" in the one I was trying to import into, so FM recognized it as a different value. Doh!