When looking through jisho.org after reading some NHK News Easy articles, I came across 楽観{らっかん}, which seems to imply optimism in terms of outlook. However, 楽天{らくてん} also carries the definition of optimism, but I'm not quite sure what the difference between the two is other than the fact that Rakuten tends to refer to the company more often than not and that 楽観 is associated with 悲観{ひかん} as an antonym.
A similar situation exists for the 的 forms of all three of these, where 楽観的{らっかんてき} and 楽天的{らくてんてき} both generally mean 'optimistic', though Jisho also notes that 楽観的 also implies 'hopeful'.
What exactly is the difference between these two when it comes to usage?