building block vs group

building block and group both are nouns.

Word	Noun	Adjective	Verb	Adverb
building block	Yes	No	No	No
group	Yes	No	Yes	No

As nouns, group is a hyponym of building block; that is, group is a word with a more specific, narrower meaning than building block:

building block: a single undivided natural thing occurring in the composition of something else
group: (chemistry) two or more atoms bound together as a single unit and forming part of a molecule

Other hyponyms of building block include chain, chemical chain, couple, unit cell, chemical group, radical, molecule.

building block (noun)	group (noun)
a block of material used in construction work	any number of entities (members) considered as a unit
a single undivided natural thing occurring in the composition of something else	a set that is closed, associative, has an identity element and every element has an inverse
	(chemistry) two or more atoms bound together as a single unit and forming part of a molecule

building block (verb)	group (verb)
	arrange into a group or groups
	form a group or group together