“aimer” is a verb. and “amour” is special, it can change its gender when set to plural. “des amours passées”
https://fr.wikipedia.org/wiki/Pluriels_irr%C3%A9guliers_en_fran%C3%A7ais

you can find love as a noun to despict a significant other in old litteracy: “mon aimée” to speak about a woman you love. not to be mistaken by “ma mie”, which has a similar meaning, but sounds like “mamie”, which means grandma.

you can speak about love of some abstract thing, then love is also a noun:

“l’amour de la peinture”

the sense of love towards other : “un amour partagé/réciproque”

“Aimer” is never used as a noun. As you pointed out, “amour” is the noun form, and while there are definitely synonyms, there is not, in French, any strict nuance between the “generic” love of somebody, the very specific love for your partner or the “love” of some generic things or concept.

Amour is not the only substantive that can be used when referring to aimer.

There is another direct derivative, amitié, which is to amour a little bit like what "to like" is to "to love" but only applies to person to person relationship (friendship) when amour might be too strong or ambiguous. There is also a stronger but lost substantive: amativité.

In all other cases, amour can always be used (son amour pour les chats, l’amour du jeu, l’amour des choses bien faîtes) but we might also use softer alternatives like attachement (e.g. son attachement pour les chats) and goût (e.g. le goût des choses bien faites).

To translate "the love for all the people", we might use:

L’amour du prochain / pour son prochain (usually in a religious context.)

L’amour d’autrui / pour autrui (ditto, expression probably a little outdated.)

L’amabilité (another aimer derivative, the quality of someone who is kind to everyone)