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

No.

The primary difference is the meaning of the word. In Brazil, "limão" typically refers to the small, green, acidic citrus fruit (known as lime in English). In Portugal, "limão" refers to the large, yellow, acidic citrus fruit (known as lemon in English), while the small green fruit is called "lima." Additionally, there is a difference in vocabulary for related items: Brazilians use "suco" for juice, while the Portuguese use "sumo."

Brazilian Portuguese Examples:

1. Eu gosto de suco de limão. (I like lime juice.)
2. Coloque um pouco de limão na comida. (Put a little lime on the food.)
3. O suco de limão está muito azedo. (The lime juice is very sour.)
4. Compre dois limões na feira. (Buy two limes at the market.)
5. Adoro caipirinha com muito limão. (I love caipirinha with lots of lime.)

Continental Portuguese Examples:

1. Eu gosto de sumo de lima. (I like lime juice.)
2. Coloque um pouco de lima na comida. (Put a little lime on the food.)
3. O sumo de lima está muito azedo. (The lime juice is very sour.)
4. Compre duas limas no mercado. (Buy two limes at the market.)
5. Adoro uma bebida com muita lima. (I love a drink with lots of lime.)