1834 Capped Bust Half Dollar

This is a pretty common occurrence. I believe that the edge lettering was applied by rolling the coin through a special machine - each side of the machine applied half of the edge lettering. Hopefully someone else can perhaps provide a more complete and accurate explanation. In any event, I have about 15 of the capped bust halves and there are variations in all of them in where the lettering stops and what divides the dollar and fifty. A couple have the dollar and fifty overlapping.

You are correct, that year of bust half dollar had vertical lines along with FIFTY CENTS OR HALF A DOLLAR imparted on the edge of the coin. There was a star in there as well. The edge lettering was imparted by what was called a Castaing machine. The edge of the coin was rolled between two linear edge dies within the machine. Not always did each coin get a full run across the edge dies, so there is quite often variation to the edge lettering from coin to coin.
They would sometimes put the coin back into the machine if they thought the lettering was incomplete. So you can often see multiple impartings, including one set right side up and the other upside down.

You should browse our 32 Day of Capped Bust Coins thread. Lots of good info and pictures of bust halves in there.