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

No.

While the core dictionary definitions of "jeito" (meaning manner, way, or method) are identical, there are significant differences in typical usage and connotation:

• Usage and Connotation: In Brazil, "jeito" is used much more frequently as a synonym for "solution" or "fix," specifically in the idiom dar um jeito (to find a way/to fix something). While a Portuguese person understands this, they are more likely to use words like solução or arranjar. Additionally, the term jeitinho refers to a specific Brazilian cultural concept (jeitinho brasileiro) involving bypassing rules via social maneuvering, a usage that does not exist in the same way in Portugal.
• Vocabulary Preferences: In Continental Portuguese, when referring to a "way" or "manner" of acting, speakers often prefer more formal or specific alternatives like maneira, modo, or forma.
• Pronunciation: There are significant differences in phonetic realization; Brazilian Portuguese is characterized by more open vowels and a more melodic, "sing-song" rhythm, whereas Continental Portuguese utilizes much more closed vowels and a stress-timed rhythm that can sound more "clipped" to Brazilian ears.

Brazilian Portuguese Examples

1. Eu vou dar um jeito de terminar isso hoje. (I will find a way to finish this today.)
2. Ela tem um jeito muito gentil de tratar as pessoas. (She has a very kind way of treating people.)
3. Não tem jeito, o computador quebrou de vez. (There is no way/It's hopeless, the computer broke for good.)
4. Ele sempre dá um jeito de conseguir o que quer. (He always finds a way to get what he wants.)
5. O jeito dele de resolver problemas é impressionante. (His way of solving problems is impressive.)

Continental Portuguese Examples

1. Eu vou encontrar uma forma de terminar isto hoje. (I will find a way to finish this today.)
2. Ela tem uma maneira muito gentil de tratar as pessoas. (She has a very kind way of treating people.)
3. Não há maneira, o computador estragou de vez. (There is no way, the computer broke/malfunctioned for good.)
4. Ele sempre arranja uma forma de conseguir o que quer. (He always finds a way to get what he wants.)
5. O modo dele de resolver problemas é impressionante. (His way of solving problems is impressive.)