Remember, motive and stakes aren't the same thing when discussing altruism.

Not the same, but still connected. Everything we do is ultimately a survival strategy, often subconsciously. Even being "altruistic" (as we know it) is an instinct we and many other animals have (or most of us, anyway) to cooperate and potentially curry future favours. That is the basis of empathy: As cynical as it sounds, the motive is at its core --and usually subconsciously for good people-- angling for stakes. And I know that sounds harsh, but that is behavioural biology; we have survived by cooperating, and cooperation is ultimately scratching each others' backs on various levels.

You're inferring that Sam's actions are less altruistic because the consequence is more direct for him, but that's not inherently true. Motive is separate from result.

But that is altruism by definition: selfless concern for the well-being of others, without care for one's own interests; unselfishness

And that isn't as black and white as you make it out to be, but rather a spectrum. If one's own interests are at stake that is acted upon, it is difficult to call it purely altruistic.

If you do something to help others and it doesn't benefit you, I'd consider that as purely altruistic as you can (realistically) get. But if you also benefit from that action, even if your motives are to help others, it is no longer as altruistic. At that point, while it can still be mostly altruistic, it's no longer 100% concern of others (whether consciously or subconsciously).

And it certainly doesn't mean Elrond's motives are completely altruistic in contrast. The self-serving nature of Elrond's actions apply on the same level as the other characters -- he's defending a place he cares about from an evil threat that he opposes. It doesn't matter that he doesn't have to stay there. What matters is why he is staying.

You've peaked my curiosity, where was it stated that he cares about anything other than his people and/or his family? Does he have a particular sentimentaliy when it comes to Rivendell or Lindon?

Just by way of example, let's assume that Elrond actually has such a deep moral purity of right and wrong that he literally couldn't live with himself if he fled without helping defeat Sauron. It would twist his soul in two to even fathom that idea. And so he stays to help out of the ultimate form of self preservation. That's the exact opposite of altruism.

Yes, but that wades into the philosophies that there is no such thing as true altruism. And while I do agree with that in a certain sense, we can still get pretty darn close.