Persil's complicated
The rights to use the name 'Persil' is owned by two different companies - Unilever (A UK/Dutch multinational) and Henkel (a German multinational).
Unilever Persil:
UK and Ireland - Top of the line front loading range of detergents.
France - High end speciality 'inspired by nature' detergent. (The equivalent of UK/IRL Persil there is Skip which is most likely the same product)
New Zealand - Top of the line range of top loading and front loading detergents. Formulation is more likely to be identical to Omo in Australia than UK/IRL Persil.
Henkel Persil:
This is Henkel's top of the line detergent in Germany, most of Europe and it's usually their prime brand in most other markets other than France (where it clashes with Unliever's TM)
I'm not quite sure who would own the TM in the United States as the product's not officially sold there. Although, I would assume Henkel might have first call.
Ariel is a TM used by P&G in quite a few markets and there may be different formulations and scents.
In general the European Ariels are all pretty much the same product.
South American and other Ariels may be completely different.