Office2013ProfessionalPlus is the MSI-based product. It cannot be activated via O365 identity. It requires KMS or MAK or ADBA.
Office365ProPlus is the C2R-based product, and can be activated by O365 identity, federated identity to your O365 tenant or by product key.
A few months ago, MSFT announced the "Shared Computer Activation" feature, and in conjunction with that announcement, that Office365ProPlus can now be used on TS/RDS installations.
Prior to this announcement, Office365ProPlus could not be installed upon TS/RDS, so MSFT were granting the use-right for Office2013ProfessionalPlus in TS/RDS scenarios. (although this required you to have or buy at least one license for it to get the product
download and product keys needed).
To the best of my knowledge, it's not at all possible to activate either of the MSI-based Office2013 products (ProfessionalPlus / Standard) via O365 identity, because MSI-based products are for perpetual licenses, where C2R O365 products are only subscription
licenses.
[OEM/OPK and Retail C2R products are different again, in that they are activated with a product key or against a Microsoft Account, not via O365]
I've never seen it stated by MSFT that O365 works with an MSI-installation. If you find that, please let us know.