slogan vs rallying cry

slogan and rallying cry both are nouns.

Word	Noun	Adjective	Verb	Adverb
slogan	Yes	No	No	No
rallying cry	Yes	No	No	No

As nouns, rallying cry is a hyponym of slogan; that is, rallying cry is a word with a more specific, narrower meaning than slogan:

Other hyponyms of slogan include catch phrase, catchphrase, mantra, battle cry, cry, war cry, watchword.

slogan (noun)	rallying cry (noun)
a favorite saying of a group, organization or individual	a slogan used to rally support for a cause
	a yell intended to rally a group of soldiers in battle