Safeway + Woolworths = Safeway?

While talking to a friend that visited Australia recently, I found out that there was a chain of supermarkets named Safeway in that country. "Safeway... Safeway... sounds familiar to me", I thought.
And yes! How wouldn't it sound familiar to me if it's the store where I buy all my groceries each week here in Canada? How great that they, apart from the stores open all across the US and Canada (which look somehow like the one on the left), have stores in Ausralia as well!
Sorry to tell, that's not the case. Or at least, it's not right now. Safeway stores in Australia were part of the US based company, but some years ago, the subsidiary company was sold to an Australian retailer named Woolworths (hmmmm... where have I heard some similar name before??).
Since then, the Safeway stores in Autralia changed their logo and they're slogan. They look like the store in the picture on the right, which is a model inspired in the Woolworths' design. The strange part of all this, is that Safeway in Australia only keeps its original name in the province of Victoria (the rest of the Safeways across Australia were renamed Woolworths). How come they're allowed to use the same name than the American company? Doesn't that infringe the trademarks rights? (Please note that, by writing down these statements, I DO NOT try to imply that Safeway in Australia, or its parent company Woolworths, are actually breaking any laws), I'm only curious to know how is this agreement (if any) actually working.

Do you know something about this strange case? Please share your knowledge through a message! Thanks!