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

No.

The difference lies in typical usage. In Brazil, "vó" is the standard, affectionate, and highly frequent way to refer to or address a grandmother in both informal and semi-formal settings. In Portugal, "avó" is the standard and much more natural term. While a Portuguese person would understand "vó," it is quite rare and is typically perceived as a Brazilianism.

Brazilian Portuguese Examples

1. Minha vó é muito carinhosa. (My grandma is very affectionate.)
2. Eu amo o tempero da minha vó. (I love my grandma's seasoning.)
3. Vó, você viu meus brinquedos? (Grandma, did you see my toys?)
4. Minha vó mora pertinho de mim. (My grandma lives very close to me.)
5. Vou levar um presente para a minha vó. (I am going to take a gift to my grandma.)

European Portuguese Examples

1. A minha avó é muito carinhosa. (My grandmother is very affectionate.)
2. Adoro o tempero da minha avó. (I love my grandmother's seasoning.)
3. Avó, viste os meus brinquedos? (Grandmother, did you see my toys?)
4. A minha avó vive muito perto de mim. (My grandmother lives very close to me.)
5. Vou levar um presente para a minha avó. (I am going to take a gift to my grandmother.)