A BATTER is an offensive player who takes his position in the batter’s box.
A batter's time at bat begins the moment the preceding batter is put out or becomes a runner. The batter becomes a batter-runner [see Rule 2.00 BATTER-RUNNER], and cannot hold the title of both batter and batter-runner simultaneously.
This distinction is reenforced by Rule 7.05(i):
Rule 7.05 Each runner including the batter-runner may, without liability to be put out,
One base, if the batter becomes a runner on Ball Four or Strike Three, when the pitch passes the catcher and lodges in the umpire’s mask or paraphernalia.
If the batter becomes a runner on a wild pitch which entitles the runners to advance one base, the batter-runner shall be entitled to first base only.
Ball four or strike three is given to the batter who cannot simultaneously be a batter-runner. There is no additional award to the batter under 7.05(i) because an unimpeded ball was pitched into the stands, deflected out of play, etc.
R1, R2. Ball four to batter skips off catcher and into the stands. Batter to first and all runners advance one base only [Rule 7.05(h) & (i)]