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

No.

While the word "bolsas" retains the same fundamental meanings in both dialects when referring to "scholarships" (bolsas de estudo) or the "stock market" (bolsa de valores), there is a difference in typical usage regarding personal accessories. In Brazil, "bolsa" is the standard and most common word for a woman's handbag or purse. In Portugal, "mala" is the much more natural and frequent term for a handbag, whereas "bolsa" is often reserved for smaller pouches or specific types of bags.

Brazilian Portuguese Examples

1. Ela esqueceu as bolsas no restaurante. (She forgot the handbags in the restaurant.)
2. Ganhei bolsas de estudos para o exterior. (I won scholarships to go abroad.)
3. As bolsas de valores estão instáveis hoje. (The stock markets are unstable today.)
4. Suas bolsas estão muito pesadas. (Your handbags are very heavy.)
5. Vou colocar o celular nas bolsas. (I'm going to put the cell phone in the handbags.)

Continental Portuguese Examples

1. Ela esqueceu as malas no restaurante. (She forgot the handbags in the restaurant.)
2. Ganhei bolsas de estudos para o estrangeiro. (I won scholarships to go abroad.)
3. As bolsas de valores estão instáveis hoje. (The stock markets are unstable today.)
4. As suas malas estão muito pesadas. (Your handbags are very heavy.)
5. Vou colocar o telemóvel nas malas. (I'm going to put the mobile phone in the handbags.)