In recent years, terahertz wave has attracted much attention and interest from the scientific community because of its important theoretical research value and broad application prospects. Terahertz spectroscopy is one of the main directions of terahertz scientific development, which is divided into two types: frequency domain spectrum and time domain spectrum. Its appearance has solved the problem of producing broadband radiation source in terahertz band, and made the terahertz fault in spectroscopy to be filled. With the development of this technology, the research about the radiation characteristics of terahertz has been gradually extended to the biomedicine, materials science, communication science, security inspection fields and so on. This paper compares the two kinds of spectrum from the production principle, performance characteristics and application ,and it introduces in detail the advantages and disadvantages as well as the superiority in some research fields of two kinds of terahertz spectrum.