For the end-user's perspective (ie, the dude who just wants to do email stuff with a mail reader like Thunderbird): It's two separate paths, as has been a normal thing for standards-based email for an eternity.
A user's inbound mail accumulates on a mail server. One server [protocol] handles getting the user's inbound mail to that user's mail client -- usually with protocols like POP or IMAP that let the user retrieve that accumulation.
Another server handles whatever mail the user decides to send, using SMTP. Each server is configured within the user's mail client, and that's just the normal way of doing things. It's ~always been split up like this (aside from outliers like Microsoft Exchange). :)
The user doesn't have to know anything about the existence or addition of a system like smtp2go. They just configure their client to send mail through mail.orgname.com (or whatever) like usual, and the back end handles the rest. Their pop/imap server address also stays the same.
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Anyway, mail servers and relays. Mail servers don't talk to eachother using things like POP or IMAP. The traditional Internet way for a mail server to send mail to another is to look up the recipient domain's MX (Mail eXchanger) entry in DNS, which specifies the inbound mail server, and just send it over using SMTP.
It was thus delivered. It was all very trusting.
That trust began to break when spam became a problem that never went away. Requirements and reputation and filtering became a serious ordeal for mail servers -- both on the sending and the receiving side of things.
Services like smtp2go can handle part of the sending-side trust-wizardry in a centralized way. They do things like maintain the reputation of their IP addresses.
In using it like this, orgname's server (which might very well be under someone's desk) ceases to directly connect to each and every recipient domain's MX.
It goes through smtp2go instead: All outbound mail simply gets routed through smtp2go, as the result of a central back-end configuration thing on orgname's mail server.
In email terms this is called relaying, though smtp2go might prefer the term smarthost[1].
Meanwhile, local internal mail (from joe@orgname to jill@orgname, say) can just get delivered locally. It doesn't have to be relayed at all. This determination is made by orgname's mail server.
And, again: The user doesn't need to know or care that their mail is/isn't being relayed, and the concept of relays themselves is as old as the hills. The user can just be happy that their mail gets where it needs to go instead of being silently dumped into a ditch, and they don't need to do anything different on their end for this to happen.