I thought of this question because both exams are for IIT and both contain subject of Biotechnology.
Gate is for M.Tech, MS and PhD admissions, while JAM is for MSc entrance.
BSc people can't go for GATE. One needs to have completed minimum 4 years of UG education to go for GATE. So, for a BSc to go for GATE he/she has to enroll for an MSc first and after MSc apply for GATE.
A BSc on the other hand can simply opt for JAM and pursue masters in IITs.