Aula vs. palestra
While both aula and palestra can be translated as lecture in English, they are used in very different contexts within a university setting. The main difference lies in the regularity of the event and whether it is part of a standard curriculum.
Aula
A1This is the standard word for a class or session that is part of a continuing course. Even if the university professor stands at a podium and speaks for two hours without interruption (the traditional English definition of a lecture), Portuguese speakers still refer to this routine session as an aula.
O professor de física dá uma aula excelente.
(The physics professor gives an excellent lecture.)
Eu faltei à aula de hoje porque estava doente.
(I missed today's lecture because I was sick.)
As aulas começam às oito da manhã.
(The lectures start at eight in the morning.)
Você copiou as anotações da última aula?
(Did you copy the notes from the last lecture?)
Na próxima aula vamos discutir o capítulo cinco.
(In the next lecture we will discuss chapter five.)
Palestra
B1This refers to a one-off presentation, speech, or talk often given by a guest speaker or at a conference. A palestra is an occasional event focused on a specific topic, rather than a recurring meeting for a graded course.
A universidade convidou um especialista para dar uma palestra.
(The university invited an expert to give a lecture.)
A palestra sobre mudanças climáticas foi muito informativa.
(The lecture on climate change was very informative.)
Depois da palestra, o orador respondeu algumas perguntas.
(After the lecture, the speaker answered a few questions.)
Vamos assistir a uma palestra no auditório principal.
(We are going to watch a lecture in the main auditorium.)
Ele viaja o mundo dando palestras sobre tecnologia.
(He travels the world giving lectures about technology.)
Summary
In short, use aula for your regular, recurring university classes that follow a syllabus. Use palestra for special, one-time talks, seminars, or presentations given by guest speakers.