Could you describe the difference between an assurance standard (ISAE 3402) vs. an attestation standard (SSAE 16)?

There is a post here that gives some background, but assurance includes both attestation and audit. Attestation services always report compliance to management's assertions to a third party. Used in this context, an audit reviews compliance of a financial statement's information to an existing standard (not simply to management's assertions). So, both an 'assurance' report and an 'attestation' report (said in context of this reference) require management's assertions. This can get very confusing, so please contact me with any questions.