Are "Theology" and "Doctrine" different?

Yes. Many Doctrines (like Calvinism or The Doctrine of the Trinity) are simply collections of multiple positions within various branches of Theology. Having the one word makes it easier to refer to each collection of parts together as a unit.

Here's some (oversimplified) examples:

• Calvinism
  • Theology Proper: God is perfectly sovereign over everything in creation and completely free to manifest his glory as he sees fit.
  • Hamartiology: Mankind is totally depraved, meaning we can't do anything good, even trust God.
  • Soteriology: God chooses to save some sinners, and he freely chooses whom he will save, without any regard for their merits (or total lack thereof). Not everyone is covered by Jesus' atoning sacrifice, but those who are will certainly believe and be saved to the very end.
• Protestantism
  • Ecclesiology: God has made all those whom he saves into a Priesthood of All Believers, none of whom is qualitatively superior to any other. Jesus Christ alone is the head of his church, not any human pope or ruling caste of human-appointed priests.