We don't have Giant Tiger here but I do remember it from Winnipeg. It was pretty depressing but the redeveloped ones from the previous page look tolerable.
I suppose our equivalent is Riff's. But I can't find a website so maybe they've since closed? That was probably the most terrifying chain I've ever been inside. You felt like you needed latex gloves just to touch anything. And the decor - both inside and out - was... rural hockey rink condemned 20 years ago.
If we're talking just a grocery, not a department store, then in urban areas here it'd be Dominion, Coleman's, and Sobeys. We have no Safeway or anything like that.
In rural areas it used to be IGA, Foodland, etc. Dominion AND Sobeys in service centres (say 5,000+ population) and possibly a Coleman's as well on the west coast of the island.
These days it seems that No Frills has cornered the rural market - and even encroaches on some suburban areas of St. John's, such as the Town of Paradise.

Marystown Mall, Google Street View
It's owned by Loblaw's, which also owns Dominion, so...