No, the oceans have specific currents. That poster is right about those, and about the fact that clines form in water - when fresh and salt water meet and haven't started mixing yet, that's a halocline, when two temperatures meet, that's a thermocline, two densities form a picocline, etc. Like, the science they're building on is all present and correct, which is why I suspect they themselves fell for the common internet myth of those photos (as a quick aside, looking at the notes, some people are getting weirdly aggressive and accusing them of deliberate misinformation, and we... shouldn't do that. This is an obvious mistake, that's all.)
They've just overstated a few parts, like this:
Oceans have their own properties as far as temperature and salinity and unless something like a storm or a current forces them to mix they won't. Mostly this applies to vertical mixing and it gives you things like thermoclines and haloclines but water is wierd and won't mix horizontally either.
They will. They absolutely will mix, even without a storm. It takes much longer without a storm, certainly, but they 100% will mix eventually. And to bring the OP's point back in, while it is true that different large bodies of water have different properties, the boundaries are far, far blurrier still, which is why there are one-, three-, four- and five-ocean models commonly used, plus others as well. Here's Wikipedia's handy model to show them:
And of course, those photos are not what is claimed - they ARE showing clines, but one is glacial meltwater meeting an ocean, and the other is sediment in a river meeting the ocean. The second one, in fact, is especially clear, because it's commonly claimed to be the Indian and Pacific oceans meeting, but they only do that around Australia and Indonesia, and there are snow-capped mountains in the background of that image.
So TL;DR - it's mostly true, except the images, and the idea that you can rigidly see or otherwise distinguish two oceans.