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

No.

While the spelling, grammar, and core meaning of "óleo" are the same in both dialects, there is a difference in typical usage. In Brazil, "óleo" is the standard, generic term used for all types of cooking oil (such as soybean, corn, or sunflower oil). In Portugal, "azeite" (olive oil) is the default and most common term for cooking oil. Consequently, a Portuguese person typically only uses the word "óleo" when referring specifically to "óleo vegetal" (vegetable oil) or technical substances like "óleo de motor" (motor oil).

Brazilian Portuguese Examples:

1. "Preciso comprar um frasco de óleo." (I need to buy a bottle of oil.)
2. "O óleo de cozinha acabou." (The cooking oil ran out.)
3. "Use óleo para fritar a batata." (Use oil to fry the potato.)
4. "O nível do óleo do carro está baixo." (The car's oil level is low.)
5. "O óleo essencial de lavanda é relaxante." (Lavender essential oil is relaxing.)

European Portuguese Examples:

1. "Preciso comprar uma garrafa de azeite." (I need to buy a bottle of olive oil.)
2. "O azeite acabou." (The olive oil ran out.)
3. "Usa óleo vegetal para fritar a batata." (Use vegetable oil to fry the potato.)
4. "O nível do óleo do motor está baixo." (The engine oil level is low.)
5. "O óleo essencial de lavanda é relaxante." (Lavender essential oil is relaxing.)