In solid-state quantum devices, superconducting nitride materials are widely used in many applications due to their suitable critical temperatures and wide range of accessible kinetic inductances. As representative material, niobium titanium nitride (NbTiN) superconducting thin films have a critical temperature up to 15 K, corresponding to a superconducting energy gap around 1 THz. In this frequency regime, terahertz (THz) spectroscopy is well matched to probe the superconducting properties below and above the energy gap, providing a direct observation via the optical conductivity. In this work, NbTiN thin films grown by plasma-enhanced reactive magnetron sputtering are studied. THz frequency-domain spectroscopy (THz-FDS) and THz time-domain spectroscopy (THz-TDS) are used to characterize a series of NbTiN thin films, including wafer-scale homogeneity mapping at room temperature and thickness-dependent superconducting properties at liquid helium temperature. We observe setup- and thickness-dependent homogeneity of sheet resistance across the 4-inch wafers. At low temperature, the superconducting energy gap and superfluid density of diced samples are derived through the complex optical conductivity, which reveals the enhanced surface boundary effect in superconducting state. Combined with transport measurements of the critical temperature, various interesting physical phenomena are gradually understood.