Syncing with Github Project Boards
Github project boards belong to a Github repository and a single repository can contain multiple project boards ( more info).
If a Github issue is added to a project boards, the column name that the issue resides in becomes the issues "status" as pointed out in the screenshot below:
Jira
When syncing Github issues with a Jira project, the column names will sync with the Jira ticket status if there is a match. This means if you have a Jira status named "In Progress" you'll also need a Github project board column named "In Progress" (case insensitive). If there is no match, Board Genius will not automatically create a new status or column for your project.

Can you only have one Kanban board per project in Jira?
Board Genius syncs with the Jira ticket status which transcends Jira boards. A Kanban board column usually reflects the ticket status. So a ticket could be in multiple Jira boards, it should have the same status.
Trello
When syncing Github issues with a Trello board, Github project board columns will me mapped to Trello board lists that have the same name. If there is no match, Board Genius will not automatically create a new list or column for your project.