The task is only seen by the people involved
Tasks are only for those who work on them. Therefore, only the responsible and the followers can see the task. Each task has one responsible person and may have several followers. If you are alone on a task (as the responsible person), no one else can see the task or open it. If there are multiple followers on a task, then each of them can see that task. Unattached tasks (that are not attached to any item) are not even visible to anyone else in the system.
In other words, access to tasks is solely at the user level and is not governed by your job title or role in the system.
How to give access to a task to someone else
If you want to give someone access to a task, you have only one option, and that is to attach them to the task as a follower or responsible person. They will then automatically see the task and receive all notifications of changes to it.
Tasks attached to an item
If a task is attached to an item, then it is visible in the task overview (i.e., others know that there is a task there), but again, only users who are working on the task can access it.