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

Yes

The meaning, grammar, and spelling of "tamanhos" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, unstressed vowels are typically more open, while in Portugal, unstressed vowels (such as the "o" in tamanhos) are much more closed or even reduced to a near-silent state.

Brazilian Portuguese Examples

1. "Essa loja tem vários tamanhos de camiseta." (This store has various t-shirt sizes.)
2. "Não encontro roupas em tamanhos maiores." (I can't find clothes in larger sizes.)
3. "Os tamanhos de calçados variam muito." (Shoe sizes vary a lot.)
4. "Eu preciso conferir todos os tamanhos." (I need to check all the sizes.)
5. "Esses tamanhos são muito pequenos para mim." (These sizes are too small for me.)

Continental Portuguese Examples

1. "Esta loja tem vários tamanhos de t-shirt." (This store has various t-shirt sizes.)
2. "Não encontro roupa em tamanhos maiores." (I can't find clothing in larger sizes.)
3. "Os tamanhos de sapatos variam muito." (Shoe sizes vary a lot.)
4. "Tenho de verificar todos os tamanhos." (I have to check all the sizes.)
5. "Estes tamanhos são muito pequenos para mim." (These sizes are too small for me.)