It is said that in IPA, each symbol represents a unique sound. But on the Wikipedia page on the Voiceless Velar Fricative (/x/), I find these examples:
Hindustani 'ख़ुशी' /xuʃi:/ (sometimes खुशी, /kʰuʃi:/) and Assamese 'অসমীয়া' (/ɔxɔmija/).
I am a native Assamese speaker and I have learned Hindi in school for ten years, and I have been regularly conversing in it for years. To my ears, these sounds are similar but clearly distinct. Even in the audio clip that accompanies the article, I feel the first part is the Hindustani ख़ while the second part is the Assamese স. I asked my friends who too are fluent in both Assamese and Hindi and they too seem to agree.
But I understand that un-systematic intuitions like the ones me and my friends are having in this case would not count as good reason to assign different symbols.
I just wanted to know the reason: if these are the same sounds, why am I so easily able to distinguish between the two? And if they are actually different sounds, why has IPA assigned the same symbol to them?