Sabab can be thought of as a mixture of the following: Cause or Occasion.While 'illa can be thought of as the Basis, or rationale for a stance or a ruling.
As brother Mohammad Saeed Al-Rahawan has mentioned:
Intoxication, and all of its personal and social ills, is the basis ('Illah) for the prohibition of Alcholol. On the other hand, Ramadan is the (Sabab)...
Sabab is used as synonym for 'illah, and the two are often used
interchangeably. Yet the ulema of usul tend to use sabab in reference to devotional matters (ibadat) but use 'illah in all other contexts. Thus it is said that the arrival of Ramadan is the cause (sabab) of fasting but that intoxication is the 'illah of the prohibition in wine-drinking.