math.random and the Random API use the same algorithm but I think it may be more than just pretty syntax? Random is an object with methods based around it, while math.random is a function and any modifiers are independent of it (such as using math.randomseed).
math.randomseed(tick()) -- Change seed relative to environment
math.random()
-- vs
Random.new(tick()) -- Change seed relative to object
Random:Next[Number/Integer] -- Get a direct number, no after-math (pun unintended)