I think the test you did, typing in both pronunciation with your input method to see if you could generate the correct glyph reveals what you need to know. In short, there are different ways to refer to different elements (e.g. radicals) of Chinese characters.
From my experience, there haven't really been any times where I would have to name a radical by its individual name (and I don't imagine most Chinese people would know these, except for maybe some very common ones). Usually I've encountered people choosing to referring to the part of a character (“语” 的左边) or simply drawing the radical on their hand, phone, etc. It would be interesting to find out if people on this site with more formal Chinese education from a Chinese speaking country are familiar with terms for radicals and such. I would guess most people that use Chinese writing frequently don't think too much about them, though.
A parallel in English to discussing radicals might be something like talking about what a "descender" is. (Google: In typography, a descender is the portion of a letter that extends below the baseline of a font.) While certainly some people with some design experience will be familiar with this term, most people just intuitively know what this thing is and work around it, by leaving room at the bottom of a piece of paper for descenders when space gets short, for example.
