It is indeed a criminal charge. By paying the ticket, you are submitting a guilty plea. A low-level charge, sure (depending on the ticket), but a charge nevertheless.
It sounds to me like all charges are criminal in your mind if they involve a finding of the court. This is not true
Just the findings that involve charges stemming from the penal code, and involve being found guilty beyond a reasonable doubt vs. the civil standard of a preponderance of evidence.