Citizens of the other five GCC states — Bahrain, Kuwait, Qatar, Saudi Arabia and the UAE — need no Omani visa at all, on either route.
Oman's foreign ministry lists 78 nationalities, including British, American, Canadian, Australian, every EU country and Japan, for a 14-day stay without a visa. Conditions apply too: your passport needs 6 months left on it, proof of a return journey, a confirmed place to stay, health cover and enough funds for the trip — and the stay can never turn into a residence visa.
A second list of 24 nationalities, including Indian, Egyptian and Jordanian passports, gets the same 14 days only when you already hold residence or a valid visa in Canada, the US, Australia, a Schengen country, the UK or Japan, or are a GCC resident in a profession Oman recognises; everyone else applies through Royal Oman Police's eVisa eligibility wizard.