Students are granted either L or B permits by the cantonal migration authorities (in Geneva, the OCPM). B permits are issued where the duration of the course of study is more than one year, which is generally the case for university studies.
Legal basis: Art. 32 and 33 FNIA
However, following the adoption of the popular initiative “against mass immigration” on 9 February 2014, the authorities seem to have started granting L permits with ever greater frequency. This practice is not in conformity with the law and should be a thing of the past. If in doubt, consult a legal advice centre.
Non-Europeans are granted biometric residence permits (with fingerprints and a photo for facial recognition stored on a chip).
Legal basis: 71d para. 1 ASE, Schengen regulation