After the Prophet, the Muslims followed different leaders. Some leaders like the Ahlul Bayt were guided by Allah. Others followed their own thinking.
It is natural that not all people will think alike. Hence these new leaders altered the original laws and 'corrected' them. Hence the different timings for different Muslims.
oh i was having this discussion the other day and i was told it is because we add 10minutes to numaaz time for precaution, as in if the sunser was 8.10 we would pray at 8.20 as the timings estimated for sunset can be wrong and it is better to pray a few minutes after the time than a few minutes early as then it would be invalid.