Any time a prosecutor drops a case they can always open it back up. "Dropping" the case just means that for some reason the prosecutor does not want to go forward with the case any longer. A typical reason is that the prosecutor determined there was not enough evidence to prosecute. So, should they come upon additional evidence, they can always recharge you.
An acquittal is different, because you have been declared innocent, and the prosecutor cannot recharge you.
The reason why your lawyer said it was basically the same thing is because they usually will not end up recharging, since they usually stop investigating and don't come up with any new evidence.

