band vs mourning ring

band and mourning ring both are nouns.

Word	Noun	Adjective	Verb	Adverb
band	Yes	No	Yes	No
mourning ring	Yes	No	No	No

As nouns, mourning ring is a hyponym of band; that is, mourning ring is a word with a more specific, narrower meaning than band:

band: jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger
mourning ring: a ring worn as a memorial to a dead person

Other hyponyms of band include engagement ring, ringlet, seal ring, signet ring, wedding band, wedding ring.

band (noun)	mourning ring (noun)
a thin flat strip of flexible material that is worn around the body or one of the limbs (especially to decorate the body)	a ring worn as a memorial to a dead person
an adornment consisting of a strip of a contrasting color or material
a restraint put around something to hold it together
jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger
a strip of material attached to the leg of a bird to identify it (as in studies of bird migration)
a thin flat strip or loop of flexible material that goes around or over something else, typically to hold it together or as a decoration
a driving belt in machinery
a stripe or stripes of contrasting color
a cord-like tissue connecting two larger parts of an anatomical structure
a range of frequencies between two limits
instrumentalists not including string players
an unofficial association of people or groups
a group of musicians playing popular music for dancing

band (verb)	mourning ring (verb)
bind or tie together, as with a band
attach a ring to the foot of, in order to identify