A square enix account is a container for all square enix online game accounts you posess. It can be used to pay for any/all of them at once.

A Square enix account is intended to be posessed by one person, however. Bear this in mind as contests/events held by the community team generally only allow one entry/participant per Square Enix account, and you can not split off service accounts from an SE account once they've been created. So, if you have a friend or significant other, they need to create their own SE account. SE accounts are not intended to be shared.

FFXI service account 2
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|-----FFXI service account 3
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Square Enix Account -------FFXIV service account 1
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|--------------------------FFXIV service account 2
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FFXI service account 1