Is there any relationship between the RSA keypair standard and RSA security?
If not, can anyone explain what RSA stands for (so I can keep the two seperate)?
In both cases (the company name and the algorithm name), the letters “RSA” stand for the initials of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman… $R$ivest, $S$hamir, and $A$dleman.
Wrapping it up in short:
Actually, there’s not much to be confused about. RSA is short for the names $R$ivest, $S$hamir, and $A$dleman. The individual context will point either to the company, or the cryptosystem.
Thinking about it, there’s only one moment where I can imagine confusion to kick in: when you forgot to concentrate while reading… as there is a bit of a difference between “RSA Security” (which points to the company) and papers talking about ”RSA’s security” (which means “the security of the RSA algorithm”).
Anyway, the articles you’ve linked to yourself already explain all that and more. Therefore, I can’t help asking myself the same question DrLecter already asked in a comment: “Did you read the two articles?”.