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.
The second tithe is a specific tithing obligation that must be separated 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.