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

No

While the spelling and fundamental meaning of "chovendo" (the gerund of the verb chover) are the same in both Brazilian and Continental Portuguese, the usage differs significantly regarding how continuous actions are expressed.

• Usage (Grammar): In Brazil, the gerund (chovendo) is the standard way to express an action currently in progress (the present continuous). In Portugal, while the gerund exists, it is much less common for describing ongoing weather or daily actions; instead, Portuguese speakers almost exclusively use the construction a + infinitive (a chover).
• Spelling and Meaning: The spelling is identical, and the core meaning ("raining") remains the same.
• Pronunciation: There are standard phonetic differences between the two variants (such as the treatment of unstressed vowels and the rhythm of the sentence), but the word itself is recognizable in both.

Brazilian Portuguese Examples

1. Está chovendo muito hoje. (It is raining a lot today.)
2. Eu não gosto de sair de casa quando está chovendo. (I don't like to leave the house when it is raining.)
3. Olha, começou a chover e agora está chovendo forte! (Look, it started to rain and now it is raining hard!)
4. A rua está ficando cheia de poças porque está chovendo sem parar. (The street is getting full of puddles because it is raining nonstop.)
5. Você viu que está chovendo lá fora? (Did you see that it is raining outside?)

Continental Portuguese Examples

1. Está a chover muito hoje. (It is raining a lot today.)
2. Não gosto de sair de casa quando está a chover. (I don't like to leave the house when it is raining.)
3. Olha, começou a chover e agora está a chover com força! (Look, it started to rain and now it is raining hard!)
4. A rua está a ficar cheia de poças porque está a chover sem parar. (The street is becoming full of puddles because it is raining nonstop.)
5. Viste que está a chover lá fora? (Did you see that it is raining outside?)