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

No

The difference lies in usage and meaning.

In Brazilian Portuguese, "presunto" is the general, standard term used for all types of ham, including the processed, sliced deli meat commonly eaten in sandwiches.

In Continental Portuguese, "presunto" refers specifically to high-quality, cured ham (similar to Spanish jamón or Italian prosciutto). When a Portuguese person refers to the processed, sliced deli meat used in everyday sandwiches, they almost always use the word fiambre.

Brazilian Portuguese Examples

1. Eu gosto de sanduíche de presunto e queijo. (I like ham and cheese sandwiches.)
2. Comprei um pacote de presunto no mercado. (I bought a package of ham at the market.)
3. O café da manhã hoje tem presunto e ovo. (Breakfast today has ham and egg.)
4. Você quer presunto no seu omelete? (Do you want ham in your omelet?)
5. Coloque um pouco de presunto na salada. (Put a little ham in the salad.)

Continental Portuguese Examples

1. Eu gosto de sanduíche de fiambre e queijo. (I like ham and cheese sandwiches.)
2. Comprei um pacote de fiambre no supermercado. (I bought a package of ham at the supermarket.)
3. O pequeno-almoço hoje tem fiambre e ovo. (Breakfast today has ham and egg.)
4. Queres fiambre no teu omelete? (Do you want ham in your omelet?)
5. Coloca um pouco de fiambre na salada. (Put a little ham in the salad.)