Chips and French fries aren't quite the same - it's a dolphins and porpoises thing. French fries would commonly be regarded as chips, but chips aren't necessarily fries.
Broadly speaking when we say chips we're referring to any hot bits of fried potato (so not cold fried potatoes referred to as chips in the US which we call crisps). Traditionally they'd be larger than French fries (maybe 1cm square and about the same length) but usually not as crispy. That's the way they're normally still served if you buy fish and chips. Sometimes they're even made from cutting up potatoes (rather than mashing and extruding them).
With the growth in popularity of McDonalds and the like in the 80s, French fries caught on. Most people would still call these chips but they're obviously different so if you want to be precise you'd use fries.
There are also larger chips (the traditional size or larger) that are fried until crispy confusing the whole matter further. These might (or might not) be referred to as chunky chips depending on where you are.
I've only been to the UK once, but I don't remember fries being called "chips" in UK McDonalds.
I've always thought of "fries" as those skinny things McDonalds/Hungry Jacks/Burger King sell, while chips are the chunkier version you get at a proper Fish'n'Chip shops or pub. Restaurants here (Australia) generally distinguish between the two.
As somebody in the UK I'd have to agree french-fried and chips are different things. One is reconstituted potatoe's into small thin like eddibles of a uniform small size and chips are cut potatoes into chunkier like bits.
Where I live, the fried potato-variant in the image is the same thing as fries - we don't distinguish between our variants. We might go as far as calling them thick fries, but that's about it.
It does seem really stupid though. Are you going to go to a fish-and-chips shop, ask for "chips but no fish", get told that they're not allowed to sell that, and then say "OK, we'll go to McDonald's instead"? That's never going to happen!
And yes, McD is being a douche bag here, but the biggest *rse is probably UK itself allowing this to happen.