[Marileangorifurnimaluim]

To draw out your most subtle point, it was a meshing of their personalities that made them so close - I agree completely. What was it in their personalities, respectively?

It was my understanding that Sam lived with his father on Bagshot Row, just below Bag End.

Even if he did live with Frodo (as they planned to in Crickhollow), that was a common arrangement with manservants in those days. (Gilthalion mentioned JRRT based the Hobbits on his youth in rural England.)

As Frodo lived with the Brandybucks until he was older, he and Sam would not have grown up together. Instead they met once he was Bilbo's ward, though class distinction is too cold a word: distinction of wealth more like. The Gaffer at the Green Dragon indicates the distinction did exist, commenting on Bilbo Baggins as being "a gentlehobbit" very respectful, unlike others he could mention. Bilbo's gifts refer to the Gamgees as being among the poorer hobbit families.

The relationship between Bilbo and the Gaffer was more formal than Frodo and Sam, (Frodo's personality makes a difference I think, growing up an orphan among a warren of Brandybucks would have made him cleave to family standing much less - family? what family? or which family? - Plus the fact he was a guest first at Bag End, before Bilbo inherited him), but still the distinction is there.

Sam's role as manservant (he did more than just tend the garden, tho' that was his main job) is indicated when he fell for Pippin's prank "Sam, it's half-past nine, have you got the bathwater hot?" It was part of a servingman's job to know their master's mind better than he knew it himself, stay one step ahead, but that didn't go the other way. "I'm beginning to learn a lot about Sam" said Frodo on the road outside Bree. That's not what you say about someone you've known well for over twenty years.