These two nouns have similar meanings, and can usually be used in place of each other, although there are some differences.
Motto and slogan both refer to short sayings (one sentence or phrase, usually) that are easy to remember and which describe a belief, policy, attitude. Both mottos and slogans can be associated with either a person or an organization.
Only mottos, however, can describe a belief that a person lives by, such as “early to bed, early to rise” or “hope for the best, but prepare for the worst.”
While only slogans are used in advertising, such as the slogan of the General Electric company, “we bring good things to life.” This includes political slogans used in political campaigns, such as “Make America great again.” Originally, the word slogan came from the Celtic languages, and referred to the battle-cries of ancient Scottish warriors.