Indeed in my courses I learned about the differences between parisyllabic and imparisyllabic, but absolutely no mention was made about i-stem!
A masculine or feminine 3rd decl. noun being parisyllabic or imparisyllabic is a pretty good determiner of whether it will be i-stem, but this isn't an exceptionless rule and it doesn't apply to neuters. The concept of i-stems is far greater than that nice little distinction.
I consider any noun or adjective with a genitive plural in -
ium to be i-stem. It may be somewhat of a misnomer, but that's how the term is consistently applied in English grammars. On the other hand, I've never found a consistently applied definition for "mixed i-stem", so I don't find it a very useful term.
There are basically three 'levels' of i-stem nouns and adjectives. On the first level, every i-stem will at the very least have -
ium in the genitive plural, and -
ia in the neuter nom./acc. plural (where applicable). So, too, may any such noun or adjective have -
īs instead of -
ēs for the masc./fem. accusative plural according to whether that rule is applied.
On the second level, some i-stems will also have -
ī in place of -
e as their ablative singular. This applies principally for neuter noun i-stems, of which only a small minority ever have -
e in their ablative singular, as well as for all i-stem adjectives* (except participles, which usually have -
e but may have -
ī when used as pure adjectives without any verbal force). On the other hand, most masculine and feminine i-stem nouns have always -
e in ablative singular (these form the group of what is usually called "mixed i-stems"), but those which end with -
is or -
ēs in their nominative singular forms may have -
ī instead of -
e in the ablative singular, but there's no consistent rule. Therefore both
igne and
ignī exist as ablative singulars, with
ignī being the older form that is more often applied in formulaic expressions, like
aquā et ignī interdicere, and used by those authors who have a tendency for conservatism in their language (Sallust, for example). Cicero and other classical authors are often inconsistent, but -
e is eventually established as the norm.
The final level is a small subset of masculine/feminine nouns ending with -
is in the nominative which have already been named above. These will will either consistently (as
vis,
sitis, and names of rivers) have -
im instead of -
em as their accusative singular and -
ī instead of -
e as their ablative singular, or only usually have them (as
securis,
turris, etc.)
*adjectives are almost universally i-stem. There are only a few exceptions, such as
vetus, which has ablative singular
vetere, genitive plural
veterum, and neuter nominative/accusative plural
vetera, as well as all the comparative forms (abl. sing. -
iore, gen. pl. -
iorum, neut. nom./acc. -
iora).