Air carrier First officer reported confusion regarding Hazmat documents provided to the flight crew. After further collaboration with Operations personnel it was determined that it was safe to continue to destination.

Narrative

As the first officer; who was not too familiar with this airport I took extra precautions to keep my focus on setting up the aircraft correct. During this time the operations agent presented the Captain with the attached form; unaccompanied baggage manifest; and advised him that the gel cell battery is permitted as a carry-on baggage and provided the Captain with the seat number. The agent continued to converse regarding this gel cell battery while the Captain was referencing chapter nine of the FOM; the dangerous goods section. Once the Captain referenced the chart (FOM) under batteries; spare/loose which states the non-spillable batteries was permitted in carry-on baggage; and the service message indicated a dry-gel cell wheelchair battery (qty 1) was on board with the seat location; we closed the door and departed.Once in cruise; the battery topic reemerged due to the new type of gel battery which has no mention in the chart that was originally referenced. Knowing that there are only three types of batteries for a wheelchair and mobility devices (dry cell/non-spillable; lithium Ion; and wet cell/spillable) there was a level of uncertainty of the gel cell battery since that label did not appear in the FOM. However; the battery powered wheelchair or mobility device tag (tag attached) does put dry cell and gel in the same category of non-spillable battery but does not appear in the battery description of the chart. By this time; it was time for my break; so the report continued to fly while the Captain contacted dispatch and the Chief Pilot who also could not provide more clarification of the issue. We continued to ZZZ and landed.