Generally the assembly is a governing body which includes student members, while the council is a 'deliberative' body that makes policy and has a smaller membership. See, for example:

El Consejo Universitario es la autoridad colegiada responsable de expedir todas las normas y disposiciones generales encaminadas a la mejor organización y funcionamiento técnico, docente y administrativo de la Universidad; conocer de los asuntos que de acuerdo con las normas y disposiciones generales, antes señaladas, le sean sometidos, y las demás que la Ley Orgánica de la Universidad le otorga, y, en general, conocer de cualquier asunto que no sea de la competencia de alguna otra autoridad universitaria.

Está integrado por el Rector y el Secretario General; los directores de facultades, escuelas e institutos; representantes propietarios y suplentes de profesores y de alumnos de cada una de las facultades y escuelas, así como de los investigadores de los institutos que realizan docencia; un representante propietario y otro suplente de los centros de extensión universitaria, cuatro representantes propietarios y cuatro suplentes de los alumnos de los programas de posgrado, y por un representante propietario y otro suplente del personal administrativo de la Universidad.
http://132.247.12.15:10003/portal

The University Assembly (UA) is a governing body at Cornell University which is comprised of 21 voting members; six undergraduate students, three graduate and/or professional students, five employees, and seven faculty.
http://assembly.cornell.edu/UA/Home

The University Council of the University of Pennsylvania is a deliberative and broadly representative forum which exists to consider the activities of the University in all its phases, with particular attention to the educational objectives of the University and those matters that affect the common interests of faculty, staff and students. It may recommend general policies and otherwise advise the president, the provost, and other officers of the University. It is authorized to initiate policy proposals as well as to express its judgment on those submitted to it by the administrative officers of the University and its various academic divisions. It is also empowered to request information through appropriate channels from any member of the University administration.
http://www.upenn.edu/secretary/council/