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

Yes

The word "outono" is identical in spelling, meaning, and grammatical gender (masculine) in both Brazilian and Continental Portuguese. The only difference is in pronunciation.

In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo "vowel reduction." This means the "o" sounds are much more closed; the final "o" sounds like a "u," and the middle "o" often sounds like a short, muffled "u" as well. To a Brazilian ear, a Portuguese person saying "outono" might sound as if they are saying something closer to "utunu."

Brazilian Portuguese Examples

1. Eu gosto muito de ver as folhas caindo no outono. (I really like to see the leaves falling in autumn.)
2. O outono deste ano está muito seco. (This year's autumn is very dry.)
3. No outono, a gente sempre usa um casaco. (In autumn, we always wear a coat.)
4. O outono chegou e o tempo esfriou de vez. (Autumn has arrived and the weather has cooled down for good.)
5. As cores do outono são as minhas favoritas. (The colors of autumn are my favorites.)

Continental Portuguese Examples

1. Eu gosto muito de ver as folhas a cair no outono. (I really like to see the leaves falling in autumn.)
2. O outono deste ano está a ser muito seco. (This year's autumn is being very dry.)
3. No outono, nós usamos sempre um casaco. (In autumn, we always wear a coat.)
4. O outono chegou e o tempo arrefeceu de vez. (Autumn has arrived and the weather has chilled/cooled down for good.)
5. As cores do outono são as minhas preferidas. (The colors of autumn are my favorites.)