As Tiago noted, these statuses were created by your company (note that the 'managed internally by JIRA Software' message is the default, and therefore highly misleading). As such, the answer to:
[...] delete one of them. Will it have any negative outcomes in the future?
It depends on what your company has done with the statuses. If possible, ask your JIRA admins what they have done with the statuses.
If that is not possible, you will have to look at all of the associated workflows of the status which you wish to delete, and check for any customized Post Functions for any transitions both going into and coming from the status-to-delete.
If you don't find any (or you find some and determine that it's still fine to delete the status), then I would suggest doing a mass-update of issues to change their status from the status-to-delete to the other status (do a search for issues via Issues->Search for Issues and then use Tools->Bulk Change).