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

Yes

The word "jardim" is identical in spelling, meaning, and grammatical category (masculine noun) in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowel "a" is pronounced with a more open sound [a], whereas in Continental Portuguese, it is more reduced or closed [ɐ]. Additionally, the phonetic realization of the nasalized "im" at the end of the word may vary slightly in intensity between the two regions.

Brazilian Portuguese Examples

1. Eu gosto de regar o meu jardim todos os dias. (I like to water my garden every day.)
2. O jardim da nossa casa está muito bonito. (Our house's garden is very beautiful.)
3. As crianças estão brincando no jardim. (The children are playing in the garden.)
4. Vou plantar algumas flores novas no jardim. (I am going to plant some new flowers in the garden.)
5. O jardim está bem grande este ano. (The garden is very large this year.)

Continental Portuguese Examples

1. Eu gosto de regar o meu jardim todos os dias. (I like to water my garden every day.)
2. O jardim da nossa casa está muito bonito. (Our house's garden is very beautiful.)
3. As crianças estão a brincar no jardim. (The children are playing in the garden.)
4. Vou plantar algumas flores novas no jardim. (I am going to plant some new flowers in the garden.)
5. O jardim está muito grande este ano. (The garden is very large this year.)