As answered on the Jira Community site:
"For a Company Managed project or a board based on a Saved Filter, the filter used by the board can be manipulated to include/exclude issues. That is one possible explanation. For a Team Managed project the native board within the project does not allow manipulation of the filter.

Additionally, issues will show up in the Backlog and on the Board only if the Status to which they are assigned is mapped to a Column of the board. Check your board settings for the mapping of Statuses to Columns and confirm that there are no Statuses listed in the Unmapped Statuses area. If they are drag them to the appropriate column of the board.

Some issue types may not display as cards on the board or in the backlog depending on the project type. Subtasks don't display as cards on the board or in the backlog for Team Managed projects, for instance.

Lastly, in a Scrum board the Backlog list in the Backlog screen will show only issues that are in Statuses mapped to any column excluding the right-most column of your board. The issues in Statuses mapped to the right-most column of your board are considered "complete" from a Scrum perspective and will therefore not display in the Backlog list. They will display in the Active Sprints in the Backlog screen. It doesn't matter if the Statuses are green/Done; it only matters to which board column they are mapped."

As this is a new board I am assigned to, I was unaware that there was a filter that was removing issues without an assigned fix version from view. Upon editing that filter, the issues were able to be seen on both Active Sprints and Backlog.