From messybeast.com, two old enclycopedia entries.
Note how the “retriever” entry shows a dog that we would now call a flat-coated retriever. From 1900 to the First World War, the flat-coat was in its halcyon days. At this time, the golden was part of the flat-coat breed, referred to as “Tweedmouth’s strain,” although Colonel Le Poer Trench’s golden dogs were registered and promoted as Russian retrievers.
Note how the 1923 entry of depiction of a retriever appears to have some wave to its coat. Fanciers had decided to breed out the wave in the wavy-coat. In flat coats, the wave has nearly been bred out, but the golden retriever, which was separated from the flat-coat before this waviness disappeared, still can come in a wavy coat.
At closer inspection it looks to me like the dogs in the pictures are identical. The latter has an increased amount of contrast, but the position, angle and look of the dog are very similar (if not identical).
The wave still exists in modern flatcoats – almost as often as in goldens. One of our boys has quite a bit of wave in his coat and has never been penalized for it in shows. In fact the wave has never even been mentioned.