universitär
university-related
Relating to a university, belonging to it, or typical of it.
Nach dem Abschluss möchte sie im universitären Bereich forschen.
After graduating, she would like to do research in the university sector.

university
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university-related
Relating to a university, belonging to it, or typical of it.
Nach dem Abschluss möchte sie im universitären Bereich forschen.
After graduating, she would like to do research in the university sector.

The adjective 'universitär' (university-related) is derived directly from the noun 'die Universität' (the university). It describes anything that has to do with a university or takes place there.
Sie strebt eine universitäre Karriere in der Physik an.
She is aiming for a university career in physics.
Common combinations are 'universitäre Ausbildung' (university education), 'universitäre Forschung' (university research), 'der universitäre Sektor' (the university sector), or 'ein universitäres Umfeld' (a university environment).
Die universitäre Lehre hat sich in den letzten Jahren stark verändert.
University teaching has changed significantly in recent years.
This word belongs to formal written language and is used mainly in academic, administrative, or official contexts.
Das Projekt wird durch universitäre Mittel finanziert.
The project is financed through university funds.
scientific
'wissenschaftlich' and 'universitär' overlap because scientific work is often done at universities. Even so, they do not mean the same thing. 'wissenschaftlich' describes the type of work: it follows methods, checks facts, and is based on research. 'universitär' describes the place or field: something belongs to a university or is typical of a university. So you can have a universitäre Veranstaltung (university event) that takes place at a university, and a wissenschaftliche Studie (scientific study) that can also be produced outside a university. The confusion arises because universities and science often occur together.

Am Abend sprechen wir über universitäre Kurse und Prüfungen.
In the evening, we talk about university courses and exams.
Für den Bericht braucht Tom eine wissenschaftliche Quelle.
Tom needs a scientific source for the report.