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

No

While the spelling and grammar of "horário" are identical in both dialects, there are differences in typical usage and meaning, as well as pronunciation:

• Usage and Meaning: In Brazil, "horário" is often used to refer to "availability" or a "specific time slot" (e.g., "Não tenho horário hoje" — I don't have a slot/time today). In Portugal, the word refers almost exclusively to a fixed schedule or timetable; to express having a "slot" or "availability," a Portuguese person is much more likely to use disponibilidade or vaga. Additionally, Brazilians may use "horário" to ask for a specific time (e.g., "Em que horário?"), whereas Portuguese people typically use "A que horas?".
• Pronunciation: Brazilian Portuguese features more open and distinct vowels. In Continental Portuguese, the "o" is much more closed (sounding closer to a "u"), and unstressed vowels are often significantly reduced or neutralized.

Brazilian Portuguese Examples

1. Qual é o seu horário de trabalho? (What is your work schedule?)
2. O ônibus chegou no horário. (The bus arrived on schedule.)
3. Eu não tenho horário para uma consulta hoje. (I don't have a slot for an appointment today.)
4. O shopping tem um horário de funcionamento amplo. (The mall has wide operating hours.)
5. Preciso mudar meu horário de almoço. (I need to change my lunch hour.)

Portuguese (Portugal) Examples

1. Qual é o teu horário de trabalho? (What is your work schedule?)
2. O autocarro chegou no horário. (The bus arrived on schedule.)
3. Eu não tenho disponibilidade para uma consulta hoje. (I don't have availability for an appointment today.)
4. O centro comercial tem um horário de funcionamento amplo. (The shopping center has wide operating hours.)
5. Preciso de mudar o meu horário de almoço. (I need to change my lunch hour.)