"Something else" x "Another thing": Qual a diferença?

It's hard to pinpoint or describe an exact rule to explain this but in general when there is a difference (they can function in the same way most of the time) I would say that "another thing" can be thought of as a "different issue", as in something you would say in a situation where you're arguing with someone and then you say for example "but that's another thing" as if saying that it's a different story, something completely different. Whereas "something else" is more about an extra alternative from a particular or general set of options, perhaps something that is different from your usual go-to choice, say if you're reading your child a bedtime story and you say "tonight I'll read you something else", or anything related to an addition to what has already been picked or selected. But like I said there isn't a exact rule and often times they can be interchangeable. It's mostly about knowing what best fits the context based on whichever option sounds more natural.

Analise estas amálgamas de frases, e tente identificar diferenças entre elas: 'Reconhecer nossos problemas é uma coisa, encontrar soluções para eles é ANOTHER THING.'... 'Eu esperava conhecer muitos lugares legais no Brasil, mas Osasco é realmente SOMETHING ELSE.'

* ANOTHER THING = uma outra coisa (muito diferente).
* SOMETHING ELSE = marcante/impressionante/incomum/excepcional/algo a mais...

Good one, however do keep in mind that this usage of "something else" is a particular expression that differs from its usual function as far as context. Most of the time it can be used similarly to "another thing", as in an additional option, something different, whatever it may be that goes along these lines. So let's not mistakingly think that that's the main difference between both and describe "something else" that way as if that's how it's primarily used.

"Something else" can also be used to describe someone who behaves (or is behaving) outrageously. For example someone at work who hides in an empty office and plays games on their phone instead of working - "Can you believe this dude? He's something else." "Another thing" is used in the expression "(you've, he's, etc.) got another thing coming." It means "you are sorely mistaken."