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

Yes

The spelling, meaning, and grammatical gender of the word "podcast" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels tend to be more open. The "o" is often pronounced as an open [ɔ], and the "a" in the second syllable is more pronounced. The "t" is typically released clearly.
• Continental Portuguese: The pronunciation is more "closed" and clipped. The vowels are shorter, and the "t" at the end of the word is often subtle or nearly unreleased, following the more consonant-heavy rhythm of European Portuguese.

Brazilian Portuguese Examples

1. Eu adoro ouvir podcasts. (I love listening to podcasts.)
2. Eu estou ouvindo um podcast muito legal. (I am listening to a very cool podcast.)
3. Esse podcast é muito engraçado. (This podcast is very funny.)
4. Você tem algum podcast para me recomendar? (Do you have a podcast to recommend to me?)
5. Eu escuto podcasts enquanto faço academia. (I listen to podcasts while I go to the gym.)

Continental Portuguese Examples

1. Eu adoro ouvir podcasts. (I love listening to podcasts.)
2. Estou a ouvir um podcast muito fixe. (I am listening to a very cool podcast.)
3. Este podcast é muito divertido. (This podcast is very funny/fun.)
4. Tens algum podcast para me recomendar? (Do you have a podcast to recommend to me?)
5. Eu costumo ouvir podcasts enquanto faço exercício. (I usually listen to podcasts while I exercise.)