My understanding is the difference is the nature of the thing you are drawing attention to, for lack of a better term. With an emphasis of matter paragraph, you are highlighting something that is already disclosed in the financials properly, but you think it's so important you should tell readers “hey look at this”. Additionally, EoMPs usually deal with items that help user's understand the financial statements. You would see things like going concern, justifies changes in accounting principles, and significant related party transactions.
Other matter paragraphs typically deal with things not disclosed in the financials. OMPs help users understand the audit, auditor's report, or auditor's responsibilities. Here you would see things like usage restrictions placed on the audit report, mention of the predecessor auditor, and when only the current period in comparative financials has been audited.
FAR - 91
AUD - 88
BEC - 86
REG - 79