What are the differences between sincerity (ikhlas) and showing off (riyaa), and what is the outcome of each?

The difference between sincerity (ikhlas (definition)) and showing off (riya') lies in the intention and motivations behind an action. Sincerity is purifying the intention behind an action, seeking only the countenance of Allah and the Hereafter. As for showing off, it is to perform an action so that people may see it and praise or glorify the doer, and it is a type of minor shirk (definition) (polytheism).

The results and effects of an action differ based on this distinction; for Allah Almighty only accepts an action performed purely for His sake. Allah has given an example of the one who shows off, saying: "His similitude is that of a hard, smooth rock covered with [a little] dust; a heavy shower falls on it and leaves it bare. They are unable to do anything with what they have earned. And Allah does not guide the disbelieving people." (Al-Baqarah: 264), and an example of the sincere one, saying: "And the similitude of those who spend their wealth seeking Allah’s pleasure and to strengthen their souls is as the similitude of a garden on a height: if a heavy shower falls on it, it yields its fruit twofold; and if no heavy shower falls, then a light rain suffices. And Allah is All-Seer of what you do." (Al-Baqarah: 265).