Hanged Man shows a man hanging upside down on a tree.  That should be quite a painful thing, but he is not really showing it in his expression. That is why, it is thought that he talks of sacrifice.  But you need to ask whether this sacrifice has any link with real suffering.

Meanwhile, Death tarot card shows the reaper riding on a horse. He is showing no mercy to those who are begging for it. This in actual life signals an end of the past or present situation. Interestingly, it is often seen that as soon as the Death tarot card appears in a love reading, the tarot reader concludes that a permanent breakup is soon going to take place between the client and her lover. Yes, depending on the surrounding cards, it can be true. But on the flip side, this specific card also signals some other meanings. Thus, the breakup might not just happen.

Apparently, there are multiple meanings hidden in both Hanged Man and Death. So going by their general interpretations is not a good idea especially for sensitive issues like feelings and relationships. Just read The Hanged Man And Death Tarot Cards In Love And Relationships to have a better understanding of what they are exactly telling you about your love life.