The second tithe is a distinct tithing obligation of 10% of the produce after terumah and the first tithe were separated. If any of these tithes were not separated, the produce was known as tevel and forbidden for consumption.
A separate 10% tithe is required from the harvest after the first tithe has been set aside.  If this second tithe isn't properly separated, the produce becomes "tevel," which is prohibited for consumption.