I think it's more that the term "fundamental right" is very powerful so all sorts of parties latch on to it to push their agenda. Free speech is not a fundamental human right. It is a fundamental right of an individual in a democracy however, very important distinction there.

There are rights that are fundamental for various reasons, but human rights are NOT rights afforded to humans, but are instead rights humans already have, simply by virtue of being humans. But since even the right to be alive can be taken away, they are universally applied to all humans, but are not universally kept by all humans. The right to live, pursue life and to pursue security of that life are some human rights, and by life or living, i mean merely existing, not dying. at the point of birth, such things are afforded to all humans. This does not mean that the rights can't be taken away, but that to take them away, one needs a reason and an authority to do so. If one commits genocide for example, there is no reason to kill random people you don't know, you may have a reason, but that reason is not related to specific individuals.

I think this is very important, because lots of really important rights exist, but they are not human rights. For example to be treated fairly, to be afforded a fair trial, to only hold sane people accountable for their actions,etc.. these are legal rights of individuals that exist within the confines of specific national structures. It maybe morally correct to treat fairly everyone, but it isn't so merely as a consequence of them being human, although I would agree that all people everywhere have that right, because it is the just thing to do.

Ultimately, it comes down to what all belief systems of all societies have in common. The things they all agree are rights of humans given to humans simply for being human, those are human rights. For a vast majority of human existence, free speech was not even a civil or governmental right, so it is hard to argue that it is a human right today. But if some day all human governments agree that all humans are afforded free speech, simply because they are humans, then it can become a human right.

Human laws are matters of humans agreeing something is a law, rights are in effects laws unto themselves, and laws that can't be enforced are just wish lists.