After much research. (MLP Wiki, the text record on Lauren Faust's commentary on NMM, & rewatching the season 4 scene of NNM/Luna's banishment.)
The even though there are lines both saying banished "in" & "to" the moon in season 1 & also in the description in MLP Wiki. The term "to the moon" can most likely be used loosely for banished "in" the moon.
As further support of the within the moon, the face of the "mare in the moon" disappearing from the moon in season-1. & the appearance of the face in season-4.
FOUND IT! *Trips, and it flies out the window* Ooops...
Well, look on the bright side. You'll be much closer now!
Narrator: And thus, the poor soldier was sent to the moon. Celestia and Luna failed to separate in time, and the kingdom was, for the first time, ruled by a double princess. Which was really two princesses joined by the cheek, but the politicians decided to call it that.
Celestia: *Starts to write a letter* Dear Princess Me, today I learnt an important lesson about friendship, specifically about personal space. It turns out cuddling someone to the point they lose their killstreak gets me thrown out a window.
*seals letter and sends it to herself*
Celestia: Oh my, a letter. Let's see what lesson about friendship I've learned today.