The requirements, responsibilities, and jurisdiction of various judicial officers vary from place to place.
In jurisdictions that use the term, magistrates are generally lower judicial officers that deal with preliminary matters such as bail hearings, administrative matters such as marriage licences, judicial authorisations such as search warrants, civil infractions such as parking violations, regulatory violations such as driving a vehicle in excess of its registered weight, and minor offences not criminal in nature.
Judges on the other hand deal with more complex matters such as civil lawsuits, lawsuits against the state, criminal trials, appeals, injunctions, challenges to the constitutionality of legislation. What matters a judge sitting on a particular court can actually hear and decide again varies from place to place.
Here in Canada we have Justices of the Peace rather than magistrates. Each province has a statutory provincial court, a superior court which is the court of inherent jurisdiction in each province, and a court of appeals. Justices of the Peace operate under the provincial courts and thus derive their jurisdiction entirely from statute. There's also the Federal Court of Canada (also a statutory court that deals with federal matters), the Federal Court of Appeals, and the Supreme Court of Canada.
The subject matter jurisdiction of each court is fairly uniform across the nation, but that's outside the scope of this post.
A justice of the peace must have post secondary education, but need not have a law degree or have been a member of any provincial bar. A judge must have a law degree, be a member of a provincial bar in good standing, and have worked as an attorney for no less than 5 years (in practice, 10 years is the minimum).