slogan vs battle cry

slogan and battle cry both are nouns.

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

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

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

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