Is the word cachaça the same in Brazilian and European Portuguese?

No

While the spelling, grammar, and primary definition of the word are identical, there is a difference in typical usage. In Brazil, "cachaça" is often used colloquially to refer to any low-quality or cheap alcoholic spirit. In Portugal, the term is much more specific, referring almost exclusively to the Brazilian distilled spirit. When referring to a generic or local sugar cane spirit, a Portuguese person would typically use the word "aguardente."

Brazilian Portuguese

1. "Vou fazer uma caipirinha com cachaça." (I'm going to make a caipirinha with cachaça.)
2. "Essa cachaça é de alambique." (This cachaça is artisanal.)
3. "Ele não aguenta nem um gole de cachaça." (He can't handle even one sip of cachaça.)
4. "Essa bebida tem gosto de cachaça de quinta!" (This drink tastes like cheap, low-quality alcohol!)
5. "A cachaça é a nossa bebida nacional." (Cachaça is our national drink.)

European Portuguese

1. "Gosto de beber cachaça brasileira." (I like to drink Brazilian cachaça.)
2. "Esta aguardente é artesanal." (This aguardente is artisanal.)
3. "Ele não suporta nem um gole de aguardente." (He can't handle even one sip of aguardente.)
4. "Isto tem gosto de aguardente de má qualidade." (This tastes like low-quality aguardente.)
5. "A aguardente é muito comum cá." (Aguardente is very common here.)