To elaborate on what Turpissimus has said...
in most people's language, "stem" and "base" are interchangeable. Technically though, the base is domin- (to which inflections are added); this is more practical because you can just add the second declension endings to it. From a linguistic standpoint, however, the terminations are the same for every declension and the variation between words is in the variation of the stem ending. From a certain view, declensions then do not even exist, just different categories of stems. This is much more than a beginner would probably want to know or even be able to understand, but the endings for the declensions are:
nominative: -s, unmodified stem (if the stem is used for nominative, the final vowel is shortened)
genitive: -s, -i
dative: -i, unmodified stem
accusative: -m (or same as nominative with neuters)
ablative: unmodifed stem
nominative: -i, -s, -a (neuter)
dative: -is, -bus
accusative: -s, -a (neuter)
ablative: -is, -bus
domino- then declines as:
the ending -os and -om change to -us and -um, but the old forms are retained in words whose bases end in v/u or qu, though modern textbooks ignore this principle. the dative and ablative plural lose the stem vowel in classical Latin, though in Greek they do not. similarly in the nominative plural of the second declension, the stem vowel is lost, though again not in Greek. I am not sure if the dative singular of the second declension was originally -oi and the i became silent as in Greek (iota subscript).
Just to show that it works with 1st declension as well:
familiai (originally familias, as in paterfamilias)
in Greek, the nominative singular of the 1st declension does carry an S ending. the -ai diphthong was changed to -ae in Classical Latin, though they would sound about the same. as in the 2nd declension, a vowel before the dative/ablative plural -is is usually dropped.
in 3rd declension, this becomes even more interesting, due to the consonant stems and i-stems (many people do not comprehend just why they are quite literally "i-stems"). The habit of stem endings to react and sometimes fuse with terminations is in fact the reason the 3rd declension is so wily.
flebile nescio quid queritur lyra, flebile lingua murmurat exanimis, respondent flebile ripae