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

Yes

The spelling, meaning, and grammatical function of "turismo" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more melodic (syllable-timed). In Continental Portuguese, the unstressed vowels are much more "reduced" or "closed," which often makes the word sound shorter and more clipped to a Brazilian ear.

Brazilian Portuguese Examples

1. O turismo é fundamental para a economia do Brasil. (Tourism is fundamental to Brazil's economy.)
2. Eu estou fazendo turismo por Minas Gerais. (I am doing some sightseeing in Minas Gerais.)
3. O turismo está crescendo muito nesta região. (Tourism is growing a lot in this region.)
4. Eles estão promovendo o turismo sustentável. (They are promoting sustainable tourism.)
5. O governo está investindo pesado no turismo. (The government is investing heavily in tourism.)

Continental Portuguese Examples

1. O turismo é fundamental para a economia de Portugal. (Tourism is fundamental to Portugal's economy.)
2. Eu estou a fazer turismo por Minas Gerais. (I am doing some sightseeing in Minas Gerais.)
3. O turismo está a crescer muito nesta região. (Tourism is growing a lot in this region.)
4. Eles estão a promover o turismo sustentável. (They are promoting sustainable tourism.)
5. O governo está a investir pesado no turismo. (The government is investing heavily in tourism.)