What is the difference between "siyam" (الصيام) and "sawm" (الصوم) linguistically and legally (in Islamic law)?

There is no difference between "siyam" (صيام) and "sawm" (صوم), neither linguistically nor in Islamic law. Both are verbal nouns from the root "sama" (صام), and they mean abstaining from food, drink, and sexual intercourse. Linguistically, it means to abstain.