A pastor is an Elder of a Christian church The word itself is derived from the Latin word pastor which means shepherd. Pastor, shepherd and elder are the same, but are not synonymous with preacher or minister.
Minister can mean several things:
Minister (government), a politician who heads a government ministry.
Minister (Christianity), a Christian who ministers in some way.
Minister (diplomacy), the rank of diplomat directly below ambassador
In general. Pastor is used more often in Christian church while minister could be a non- christian.