These various short sea vessels docked in Millbay docks, but the ocean liners anchored out in the Sound. After 1900 both the GWR and the LSWR provided separate tender vessels, an agreement was the GWR carried the mails and the LSWR the passengers. The LSWR new and palatial dockside station was at Stonehouse; the GWR, not needing such an elaborate arrangement for its inanimate cargo, just unloaded at Millbay quayside where there were tracks alongside. Millbay passenger station itself was a bit inland, outside the docks, it fell into local use only and was closed after 1939, the dock tracks running past the station.
The LSWR branch to Stonehouse, about a mile west of Millbay, was a right nuisance, corkscrewing round existing buildings, and rising up in Devonport LSWR station goods yard, after tunnelling right under the main goods shed, facing the wrong way, towards North Road, so a docks pilot loco had to pull the special liner train up through there, where the train loco came on the other end to depart via Okehampton. The LSWR lost a lot of money on their venture, and shortly after the GWR became the much shorter route through Castle Cary they gave up and the GWR took the passengers as well.
The advantage of Plymouth for liners was not just the shorter sea distance compared to Southampton, but the liners mostly served both Britain and France, even if based at Southampton they were a lot quicker getting people and mail to London if they stopped at Plymouth first, then went to Cherbourg, and finally home port in Southampton. French ships likewise did Plymouth, then Cherbourg, avoiding a dog-leg trip across The Channel. Even Queen Mary/Elizabeth normally served Cherbourg on their Southampton voyages. Anchoring in Plymouth Sound instead of tying up saved several hours as well. The GWR thought they could do the same with liners heading to Liverpool, and developed Fishguard, but that was even less successful for ocean traffic than Plymouth. One traffic the LSWR retained was a courier would pick up all the freight documentation from the ship, and travel straight to Southampton with it, starting the customs clearance process in advance and saving a day or more of paperwork delays when the bulk freight was being finally unloaded there. Obviously this transferred to sending these advance documents by air.
I'm probably one of the few here who can recall the Ocean Liner Specials, which ceased in 1963 and were pretty few and far between at the end. The Up services typically came through Taunton at lunchtime, following one block behind the nonstop Cornish Riviera Express, so all the Up distant signals came off twice in about 5 minutes. Always a Castle to the end, immaculately polished, cleanest loco of the week, a credit to the Laira team. The old Ocean saloons, still in brown/cream livery, were likewise, maybe just four of them and a van.