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

Yes

The spelling, meaning, and grammar of the word "iogurte" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese: In most Brazilian dialects, the "t" is palatalized, sounding like the "ch" in "cheese" ([i.o.'ɡu.tʃi]). The final "e" is pronounced as a clear, unstressed [i] sound.
• Continental Portuguese: The "t" is dental (the tongue touches the teeth), and the final "e" is a closed, unstressed [ɨ] sound, which sounds much more muffled or nearly silent to an untrained ear.

Brazilian Portuguese Examples

1. Eu gosto de comer iogurte com frutas. (I like to eat yogurt with fruits.)
2. Você comprou iogurte de morango? (Did you buy strawberry yogurt?)
3. O iogurte está na geladeira. (The yogurt is in the fridge.)
4. Vou tomar um iogurte no café da manhã. (I'm going to have a yogurt for breakfast.)
5. Este iogurte está muito azedo. (This yogurt is very sour.)

Continental Portuguese Examples

1. Eu gosto de comer iogurte com fruta. (I like to eat yogurt with fruit.)
2. Compraste iogurte de morango? (Did you buy strawberry yogurt?)
3. O iogurte está no frigorífico. (The yogurt is in the fridge.)
4. Vou comer um iogurte ao pequeno-almoço. (I'm going to eat a yogurt for breakfast.)
5. Este iogurte está muito azedo. (This yogurt is very sour.)