The Olympic Hot Springs Road is sometimes seen referred to as the Elwha River Road. Locals are not affected … even though they also practice & perpetuate the ambiguous usage.
The road that visitors to the Olympic National Park and the facilities & recreation along the Elwha River will be looking for is the Olympic Hot Springs Road. Not the Elwha River Road.
There are roads outside the Park, near and around the lower, downstream reaches of the river, one or more of which at various time have been called Elwha River Road … but the one going into the Park has been the Olympic Hot Springs Road, since early in the 20th C.
Verily, there is also the Olympic Hot Springs Abandoned Trail, which the road superceded with the same destination, and inherited the name.