It is possible for people to disagree on this issue. However, the general idea is that Clinton’s transgressions were not as directly related to governing as were those of Nixon.
In the Watergate scandal, Nixon’s wrongdoing was very closely connected to governing. The original crime was committed in order to help Nixon defeat his political opponents. He then used the power of his office to prevent the investigation from proceeding. These were examples of him using his actual presidential power for illicit ends.
By contrast, Clinton’s transgressions were much more personal. The underlying problem was based on marital infidelity. Clinton then lied, essentially as a public citizen, when questioned about the infidelity. He did not use his presidential powers to try to impede the investigation. He did lie, but he did not try to abuse his power.
For these reasons, Clinton’s crimes were not seen as sufficiently bad to warrant removal from office.