Whether the vowel this letter writes is a distinct unit of the sound system, or a variant of i conditioned by the consonant in front of it, is one of the longest running arguments in Slavic phonology, and the alphabet took a side more than a thousand years before the argument started.
The case for treating it as a variant is distributional. In Russian it never appears after a soft consonant and i never appears after a hard one, so the two are in complementary distribution: knowing the consonant tells you which vowel follows, and no pair of words is distinguished by the choice alone in ordinary circumstances. On that reasoning the two are one thing wearing two coats, and the difference belongs to the consonant.
The case for treating it as its own unit is that speakers hear it as a separate vowel, that it behaves like one in borrowings and in words standing alone, and that the complementary distribution has exceptions once the whole vocabulary is admitted rather than the core of it.
The two positions are associated with the two great schools of Russian phonology, and the disagreement is a genuine one about how much of a sound system belongs to consonants and how much to vowels, not a quarrel over terminology.
The alphabet is a witness on one side. Writing this vowel as the hard sign plus i is precisely the analysis that treats it as an i modified by an unsoftened consonant, and whoever devised that spelling in the ninth century had reached that conclusion by ear alone.