Luther and Calvin's views are both Protestant, in that they differ from the Roman Catholic Church's orthodoxy. Their views are different and started movements that still have an impact on theology today.

They most prominently differed theologically in regards to how Salvation was received.

The traditional Roman Catholic view is that Salvation through Christ (which gives you access to eternal life) is a combination of faith in Christ, and your works as a human on earth. They believed that there were certain actions, like deadly sins, which could separate you from God if committed and remained unconfessed. Also, emulating Christ would bring you closer to God, which is why much of the clergy has the traditions that they do. Also common at the time of Luther were actions that you could do to help earn your way out of purgatory (like indulgences). Ultimately, you had a certain level of free will to choose what you did with your life, and your choices, including your choice for faith, were what mattered most.

Luther's viewpoint was different. His view was that Salvation was by faith ALONE, something which was a big deal to the theological discussions of the day. To Luther, works were irrelevant because humanity is so far gone in its sinfulness that it would be an impossible task to ever please God with good works; our evil would always far surpass our good. His emphasis on faith alone is one of the biggest pillars of the Protestant movements going forward. He still believed that it was a free will choice to have faith, and that accepting Christ and having faith in Christ was the most important part of being a Christian.

For Calvin, he believed similarly to Luther, but rejected the idea of free will, leading him to espouse a doctrine known as Predestination. The premises for the idea of predestination are that ultimately, God is all knowing, and all powerful. This means, that no matter what you choose to do, God already knows what you will choose (due to his omniscience). Also, God is all powerful, meaning that everything that is, he allows and wills to happen. This leads him to believe in Predestination: there are the elect whom God has chosen to go to heaven, and those whom God has chosen to receive eternal damnation. This leaves out free will and is a far more deterministic view of God and humanity.

I hope this helps! Ask away if you have more questions, I am more than happy to answer.

I see this whole question differently.

First, I am not convinced Calvin and Luther themselves saw any great tension in their beliefs about justification or about the doctrine of election. The Internet’s obsession with these issues, especially in simplistically identifying “Calvinism” with an astringent and abstract double predestination, is a projection back onto Calvin of ideas from later Calvinists that were not central to his own thought. Did Calvin accept “double predestination”? Of course. But it did not mean to him what it did to, say, the Westminster divines. Nothing about the doctrine of justification, including the idea of election, was as important to Calvin as it was to Luther, and it certainly was not as important to him as the ecclesiological matters that really focused his attention.

The only issue that really divided Luther and Calvin in a fundamental sense was the differing ways they understood Christ to be present in the Lord’s Supper. Even this was originally a disagreement between Luther and Zwingli, both of whose positions Calvin came to reject.

Luther believed the presence of Christ in the communion elements was real and physical, though the elements remained bread and wine (in contrast to the Roman view that they became in essence the flesh and blood of Jesus while keeping the sensible traits of bread and wine). He did this by transforming the idea of the “communication of properties” from a rule of speech (which it had been in the ancient church) into a straightforward description of reality. Cyril of Alexandria had clarified that one could say that “God wept,” because Jesus wept at the tomb of Lazarus. It is an appropriate way of speaking because of the union of the two natures. The man Jesus wept, and because his humanity had been assumed by God in a personal union, we could say that in that sense God wept. Using that same logic, Luther wants to say that Jesus is (or can be) everywhere at once, because God can be. As God had assumed the human nature of Jesus, you could say Jesus is everywhere. Luther then turned this into a straightforward description of reality. Jesus can be physically present everywhere the Lord’s Supper is celebrated, and his flesh and blood could therefore be received with the bread and wine whenever it is celebrated. Luther believed it was important to be able to say that even an unbeliever who takes the elements receives the flesh and blood of Christ. That was a kind of test question for him.

Zwingli thought this was all perfect nonsense and taught that the bread and wine are symbols. The presence of Christ is a mental exercise, and not real in any sense.

Calvin took a position between these, though whether he intended this as a compromise or not is debated. His view was that there was a close connection betweens the sign and the thing signified, but that the signs (bread and wine) were physical and the thing signified was spiritual. The handy tag the tradition has hung on this view is “spiritual real presence.” As Calvin saw it, Christ was spiritually present to the congregation in the celebration of the Lord’s Supper in a distinctive way that went beyond the everyday presence of Christ in a believer’s life.

Luther lumped Calvin in with “the sacramentarians,” (by which he meant everyone who didn’t believe some kind of physical real presence) and rejected this teaching completely. Calvin reached out to others in the Swiss Protestant community to try to find ways to overcome their differences and he did reach an agreement with Bullinger, Zwingli’s successor at Zurich, the Consensus Tigerinus, but this was never very satisfactory to anyone.

This is obviously a bunch of theologia, and it's hard for people in our time and place to see why it was so important in theirs, but it made sense to them. It was the one really significant issue that insurmountably divided Luther and Calvin. This difficulty is why I was slow to respond here, but since the discussion seems to have taken off I figured I would throw it into the pot.

EDIT: TL; DR: Calvin wasn't interested in the same things Luther was. The only thing they really disagreed about was where Jesus was when a congregation celebrated communion.

To go into more detail on Luther and Calvin's views on Predestination

For Luther, Christ's death was for all of humanity but the elect were predestined by God to have faith (although they still had free will to reject that gift). Faith after all, was a free gift from God and was not in anyway earned by the elect.

Calvin takes this a step further and says that not only are the elect predestined to have faith (and cannot reject it) but that most would be predestined by God to go to Hell, where God could exercise his wrath, and justice on sinful man. In this view Christ's death was for the atonement of only the elect. God is still seen as merciful though because he rescues some sinful humans from the fate they deserve.

Edit: If you want to look up more info, Luther's view is known as single predestination while Calvin's is double predestination