I wonder why you want to compare these two terms. To cover the first part, here's a link: What is embedded consensus ? As far as sidechains are concerned, idea stems from the question: What if you could transfer your Bitcoin directly to other blockchains? In case that you wanted to use the features of blockchain Y and you wanted to avoid the risk of purchasing those tokens, you could use your coins directly via two-way-peg. A very interesting sidechain 'attempt' at the moment is RootStock.