Different zetas？

Why do the existing code versions use different zetas from Appendix A of FIPS203? The range of zetas in 203 is from 0 to q-1, and the code is - q/2-q/2. Is this because different reduction methods are used? And I noticed that MultiplyNTTs uses a new zetas table in FIPS203, while the code still uses a part of the same zetas as NTT. Why is this done? Looking forward to your response.