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

Yes

The word "velejar" has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese: it means "to sail" (specifically using sails). There are no differences in how the word is written or its fundamental definition.

The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and the rhythm is more syllable-timed, making the pronunciation clearer and more melodic. In Continental Portuguese, the unstressed vowels are often reduced or "swallowed," and the rhythm is more stress-timed, resulting in a more clipped and consonant-heavy sound.

Brazilian Portuguese Examples

1. Eu adoro velejar no mar de Angra. (I love sailing in the sea of Angra.)
2. Nós estamos velejando desde o amanhecer. (We have been sailing since dawn.)
3. O vento está perfeito para velejar hoje. (The wind is perfect for sailing today.)
4. Ele quer aprender a velejar nas férias. (He wants to learn how to sail during the holidays.)
5. Vamos contratar um barco para a gente velejar. (We are going to hire a boat so we can sail.)

Continental Portuguese Examples

1. Adoro velejar no oceano. (I love sailing in the ocean.)
2. Estamos a velejar desde o amanhecer. (We have been sailing since dawn.)
3. O vento está ótimo para velejar hoje. (The wind is great for sailing today.)
4. Ele pretende aprender a velejar nas férias. (He intends to learn how to sail during the holidays.)
5. Vamos alugar um barco para velejar. (We are going to rent a boat to sail.)