There are two things you might be talking about here, but I am not sure which it might be.
The first is the parent/child relationship that issues with their sub-tasks. The Issue level issues are said to have "child" sub-tasks, and a sub-task is said to have a "parent" issue.
The second is issue links - you can define many types of issue link, and they are directional, displaying a different name depending on which end you are looking at. For example, if you have a "dependency" issue link type, you would usually find it set up to show like:
Same link, but looks a bit different depending on which end you are looking at.
Your administrators can control the list of available issue link types, and they're the people to ask when you have an unclear one.
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