I was reading a Latin grammar book (Jenney's First Year Latin, for the curious) having recently resolved to learn a bit about the language and what I understood was as follows:
Latin is an inflected language, i.e., conjugations for verbs and declensions for nouns/adverbs/pronouns. I've studied some Spanish in school so here my understanding is basically "declensions are conjugations, i.e., different endings depending on tense, but for parts of speech other than verbs".
There are different cases for the declension - much like Spanish has the imperfect, present, present progressive, preterite, etc tenses for verbs, Latin has nominative, dative, accusative, ablative, vocative, genitive.
There is gender - masculine, feminine, and neuter - much like how Spanish has gender (though it doesn't have the neuter gender, but I mean it affects more parts of speech than it does in English).
There are different cases for the conjugation - perfect, etc.
This all made sense to me, so I continued to the first "lesson", entitled "first declension; nominative case" and read "the first declension - nouns whose stem ends in -a belong to the first declension ..."
This threw me off. My understanding is that declension literally just means that there are different cases for nouns/adverbs/pronouns, much like conjugations means there are different tenses for verbs which result in different endings depending on the subject (again, I go back to Spanish - in the present tense for the subject "yo" the verb "nadar" becomes "nado" or similar) but this seems to imply there's more to it. Some googling brought up that Latin apparently has five declensions (but six cases? my original understanding led me to conflate case and declension, apparently).
What exactly does this idea of the 'declension' mean? Does this correspond to (e.g.) -er, -ir, and -ar verbs in Spanish (endings of the infinitive)?