Dezessete vs. dezassete
The Portuguese words dezessete and dezassete both mean seventeen. The difference between them is not one of meaning but of regional standard, specifically distinguishing Brazilian Portuguese from European Portuguese.
Dezessete
A1This is the standard spelling and pronunciation for the number seventeen (17) used in Brazilian Portuguese.
Minha irmã tem dezessete anos e já sabe dirigir.
(My sister is seventeen years old and already knows how to drive.)
O voo para Lisboa sai do portão dezessete.
(The flight to Lisbon departs from gate seventeen.)
Eu comprei dezessete pães para o café da manhã da família.
(I bought seventeen bread rolls for the family's breakfast.)
A temperatura máxima hoje será de dezessete graus Celsius.
(The maximum temperature today will be seventeen degrees Celsius.)
Dezassete
A1This is the standard spelling and pronunciation for the number seventeen (17) used in European Portuguese, as well as in African and Asian Lusophone countries.
O meu filho faz dezassete anos na próxima semana.
(My son turns seventeen next week.)
Ele mora no número dezassete da Rua das Flores.
(He lives at number seventeen on Flores Street.)
Faltam apenas dezassete euros para eu poder comprar o jogo.
(I'm just seventeen euros short of being able to buy the game.)
A equipa marcou dezassete golos ao longo do campeonato.
(The team scored seventeen goals throughout the championship.)
Summary
To summarize, the core difference is geographical. Dezessete is the correct and exclusive form for the number 17 in Brazil. Dezassete is the correct form in Portugal and other countries that follow the European Portuguese standard. Both words are pronounced slightly differently due to the vowel change (e vs a), but they are mutually intelligible and mean exactly the same thing.