No difference. Both are perfectly acceptable and legal. The main difference is that the parallel importer needs to set up and maintain their own workshop and handle all your warranty and servicing work. Otherwise you can pay an “adoption fee” to the appointed distributor which is usually exorbitant ($10,000 or more) to undertake your vehicle into their service program. You just need to do your homework to ensure you choose a parallel importer who has a strong history and reputation. Many have been around for 20-30 years successfully. Longer than the official dealer actually!
Tax implications are the same. And in fact dealer is often more expensive for the same product because they have both the markup from the official importer/distributor and their own markup as the official dealer!
Vehicles are registered as “new” and you are the first owner (no transfers). In some cases they do come in as a “used” vehicle even if they are new - this happens when they have been registered in the U.K. or Germany or wherever they are imported from - but I stay away from those. I think dealers in U.K. have a time limit on how long they can keep a car in their inventory and not register it. That’s why this sometimes occurs.
Taxes, duties and registration/tag fees in Singapore are sky high. Just to give you an idea, my 2020 A45S Plus was on the road for GBP 170,000. An AMG GT S is about GBP 675,000 on the road!! My Porsche Macan GTS was GBP 250,000 on the road.
I would imagine more reasonable in U.K.!