Yes, for the vast majority of tourists, a visa for Dubai and Abu Dhabi is exactly the same. The United Arab Emirates (UAE) operates under a unified federal visa system, meaning that a visa issued by any of the seven emirates is valid for travel throughout the entire country. If you apply for a tourist visa through an airline like Emirates (based in Dubai) or Etihad (based in Abu Dhabi), you are granted a UAE Entry Permit that allows you to land in one city and depart from another, or travel by road between them without any additional paperwork. This also applies to travelers from countries eligible for a "Visa on Arrival"; whether you land at DXB or AUH, you receive the same 30-day or 90-day stamp that covers your stay across the whole nation. The only distinction is the issuing authority listed on the document (e.g., GDRFA for Dubai vs. ICP for Abu Dhabi), but functionally, there are no internal border checks or regional restrictions for legitimate visa holders.