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

No

While the fundamental meaning of "velha" (old, feminine) remains the same in both dialects, there are significant differences in typical usage and connotation.

In Brazilian Portuguese, "minha velha" is a very common, colloquial, and often affectionate way to refer to one's mother. It is also frequently used as slang to refer to a long-term partner or wife. Because of this, the word carries a level of intimacy in Brazil that it does not have in Portugal.

In Continental Portuguese, calling your mother "velha" is much less common and can be perceived as rude or purely descriptive of her age. A Portuguese person is much more likely to use "mãe" (mother) or, when referring to an elderly person, "idosa" (elderly) or "senhora" (lady) to maintain politeness. Additionally, the grammatical construction of continuous actions differs: Brazilians use the gerund (fazendo), while Portuguese people use the preposition a + infinitive (a fazer).

Brazilian Portuguese Examples:

1. "Minha velha me disse para não chegar tarde." (My mom told me not to arrive late.)
2. "Essa roupa velha precisa ser jogada fora." (This old clothing needs to be thrown away.)
3. "A minha velha faz um feijão delicioso." (My mom makes a delicious beans dish.)
4. "Ela é uma mulher velha, mas muito forte." (She is an old woman, but very strong.)
5. "A minha velha está preparando o almoço." (My mom is preparing lunch.)

European Portuguese Examples:

1. "A minha mãe disse-me para não chegar tarde." (My mother told me not to arrive late.)
2. "Esta roupa velha precisa de ser deitada fora." (This old clothing needs to be thrown away.)
3. "A minha mãe faz um feijão delicioso." (My mother makes a delicious beans dish.)
4. "Ela é uma senhora idosa, mas muito forte." (She is an elderly lady, but very strong.)
5. "A minha mãe está a preparar o almoço." (My mother is preparing lunch.)