There’s a whole set of distinctly British retail terms. One is “offer” for the American “sale.” The other is “range” to mean (in the OED’s definition) “A set of goods manufactured or for sale.” (The dictionary quotes this quintessentially British line from a 1963 issue of Punch: “Harvey Nichols have a new range of Californian swimwear.”)
Both of them turned up in an advert in today’s Philadelphia Inquirer.
I know Dyson originates in the U.K. but still, gee whiz.
notoneoffbritishisms.com 
Use of the word ‘range’ may be a Britishism but I don’t recall seeing the phrase ‘shop the range’ anywhere over here. (I’ve now got ‘Shop, shop on the Range’ going through my head,)
I was going to say the same thing and today I just received an email from eBay saying ‘shop this sale’ and ‘shop it all’. I’ve never heard these expressions before…
You might “see our range” or “view our range”, but never “shop the range”.
Also, “offer” and “sale” aren’t synonyms in British English. A sale is an event, often linked to the calendar (summer sale, the Christmas sales), or circumstance (closing-down sale), whereas an offer is specific reduction on an item, which may be part of a sale (special offer, half-price offer).
Range can be a subset of the goods offered – for example “organic range of sheets” or “range of children’s sheets”. There’s usually some sort of commonality between the items in the range.
Sale is ambiguous. If someone says a product is on sale at Tesco’s, that could either mean it’s on offer or just that the product is being sold there. By saying it’s on offer, that clears up the ambiguity.
I’m guessing the equivalent US term for a range would be a line. You may think range is bad but we have to put up with the BBC News telling us that stores (aaagh…it’s shops!) will be open on Boxing Day.
There is actually a chain of shops in UK called The Range.
It sells homewares.
“Homewares”?
I think we’d probably just say “buy”. Saves on ink.
Referring to the picture above, we now have Black Friday here in the UK. We don’t have thanksgiving, but we do now have the opportunity to fight over large screen TVs at low-rent supermarkets.
Here’s a summary of U.S. uses:
“For sale”: available for purchases (equiv. to Br. “on offer”?– or does “on offer” imply a reduced price?)
“On sale”: could mean either the same as “for sale” or “offered at a reduced price.”
“Sale” (noun): “A sale” is an event usually lasting one day or more in which various items are offered for reduced prices
“Line”: equiv. to BrE “range.”
Yes, *on offer* isn’t the ordinary general “for sale”, meaning the goods offered by a retailer for customers to purchase: it implies something different from the normal price or terms of sale; it could be a straightforward price reduction per item or a buy one get one free or a three for the price of two, a special one-day only price or a special introductory price for a new line or range. In a large supermarket you will also see prominent red signs with the word “OFFERS” at the end of some aisles, signalling some special deal on certain items.There are certain legal requirements, such as that goods must have been for sale for a certain minimum number of days at a higher price before they can be advertised as being at a reduced or “sale” price but there is still plenty of scope for luring people into buying more with offers which can be confusing if not downright misleading. “Managers’ Choice” is a label they sometimes stick on shelves which appears to be some kind of offer but means nothing at all.
In short: US “on sale” = UK “on offer”. UK “on sale” = US “for sale”.
The picture is not really a Britishism.
“Offer” has been used in American ad copy for a long time as a legal-sounding term for a time-limited, special price or deal on a single item. In the sense of:
“13. (law) a proposal supported by adequate consideration, the full and complete acceptance of which constitutes a contract”
So “Offer not valid in Florida, etc.” Or “offer valid through…”
“On offer” for “on sale” would be a Britishism, though.
Reduced prices are “on special offer” in the UK, or just “on offer”. Curiously, in Australia, they are “on special”.
In the UK, I’m sure I’ve heard “offer” meaning a range of different products in a business management context too: a CEO might say “We have changed our offer to reflect the expectations of our customers.”
“Offer” and “sale” aren’t interchangeable in British English. We use “sale” when many items are (allegedly) discounted, but “offer” when a lower price is limited to one or a few items. These could be also be referred to as “special offers”