Software projects use Issue Tracking Systems (ITS) like JIRA to track issues and organize the workflows around them. Issues are often inter-connected via different links such as the default JIRA link types Duplicate, Relate, Block, or Subtask. While previous research has mostly focused on analyzing and predicting duplication links, this work aims at understanding the various other link types, their prevalence, and characteristics towards a more reliable link type prediction. For this, we studied 607,208 links connecting 698,790 issues in 15 public JIRA repositories. Besides the default types, the custom types Depend, Incorporate, Split, and Cause were also common. We manually grouped all 75 link types used in the repositories into five general categories: General Relation, Duplication, Composition, Temporal / Causal, and Workflow. Comparing the structures of the corresponding graphs, we observed several trends. For instance, Duplication links tend to represent simpler issue graphs often with two components and Composition links present the highest amount of hierarchical tree structures (97.7%). Surprisingly, General Relation links have a significantly higher transitivity score than Duplication and Temporal / Causal links. Motivated by the differences between the link types and by their popularity, we evaluated the robustness of two state-of-the-art duplicate detection approaches from the literature on the JIRA dataset. We found that current deep-learning approaches confuse between Duplication and other links in almost all repositories. On average, the classification accuracy dropped by 6% for one approach and 12% for the other. Extending the training sets with other link types seems to partly solve this issue. We discuss our findings and their implications for research and practice.