Can anyone, please, explain the difference between CAST jobs and Temporary ones?
Under which circumstances should one apply for one or another?
It's simple. As a temporary agent you work on the conditions of the official basically (salary etc.). The only difference is, that it's "temporary". Usually temporary agent positions are in places where a job cannot be guaranteed after some time - e.g. often in the EP (your work is limited to the term of office of the Parliament) or in the cabinets of Commissioners who are there only for 5 years.
Contract agents have less pay and benefits. The vast majority of contracts is granted as contract agent than temporary agent as contract agents provide "cheap" labour. There is no very clear logic there.
If you want to work for the Institutions, this doesn't change anything from a perspective of an applicant. If there is a position, you are free to apply (unless clearly written that the position is for those already employed by the institutions). The only real difference is the salary.
Ada, thank you for your answer and info provided.