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This is fetching an array; I would assume, from the Dolphin site of the user trying to connect using Dolphin Connect module.  Is that correct? 

Correct.

OK, this is an integer by the i and from the name I would think it is a UNA ID; not the Dolphin ID 

Correct, this is the result of the following query:

SELECT `local_profile` FROM `bx_dol_accounts` WHERE `remote_profile` = $iRemoteId

Exactly what are we comparing here from both the UNA side ...

The mentioned table `bx_dol_accounts` keeps the Dolphin id and the current profile id from the UNA created for this "connected" user. There is no situation to use the Dolphin user ID directly in the UNA.