I would like to know if there is any dialectal use of the words poupar aforrar and economizar.
I am under the impression that the word poupar is more used in European Portuguese while economizar is more used in Brazil. Is it right?
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Some notes from the top of my mind (the question would deserve a more in-depth study):
"Aforrar" is something I never heard, or read for that matter.
So, if it exists, it must be "dialectal", and either restricted to a quite small region - because I never heard it in Brasília, Porto Alegre, or Rio de Janeiro, or from acquaintances from the Northeast or São Paulo - or to a very informal register - because I have never read it in texts of Brazilian, Portuguese, or African writers.
The other two words are both widely used, as far as I know, in all Lusophone countries, and in all contexts and registers, formal or informal. But while their meaning is very similar, they cannot be used interchangeably in every context, though the differences are subtle, and mostly in emphasys.
I am not sure that the explanation in a comment above ("poupar" is for money, "economizar" is for resources) is true. To me, it sounds perfectly natural to say "economizou muito, a fim de não passar dificuldades na velhice", as it is to say, "precisamos poupar água". The main difference seems to me to be that "economizar" may mean simply not spend too much, while "poupar" means to set the unused money, or resource, apart, in a planned way. But perhaps this varies within different regions.
One difference that I see is that "economizar" is preferred when the meaning is intransitive (with the implication that the unstated object is money): "ele não sabe economizar", while "poupar" usually needs a complement.
"Poupar" is often used with an indirect object, too ("ele não poupava sofrimentos aos pais"). The use of "economizar" in this way, while certainly possible, is more rare.
Plus, "economizar" often comes with complements with the preposition "em": "não economizou nos adjetivos ao denunciar os absurdos da sentença"; this is avoided with "poupar": "não poupou os adjetivos ao denunciar os absurdos da sentença".
Another difference is that "poupar" can be used as an equivalent of English "spare": "poupe-me a demagogia", "spare me the demagoguery"; "poupou-lhe a vida", "she spared his life" (and in this sense, it is often intransitive, too: "poupe-me"). "Economizar" definitely cannot be used like that.