Holy is from "heileger" meaning "holy" in German.
Ghost is from "Geist" meaning "spirit" or "ghost" in German.
Spirit is from the Latin "Spiritus" meaning "spirit" or "ghost".
It's clunky to use one Germanic word and one Latin word. It should be "Sanctified Spirit" or something if you're going to go the Latin route.
Long story short, they are equivalent, they just come from 2 different language families (Latin/Romance languages, and German)
Because of its dual "mutt" heritage as a language, English has a minimum of 2 words for almost everything. The low-end, usually 1 syllable from Anglo-Saxon (German), and the high-end, fancy, educated, polysyllable word coming from Latin through the Romance languages, especially French (Thanks, Norman invasion!)
sweat/perspiration
car/automobile
mouth/orifice (from os, oris - "mouth" in Latin)
smart/intelligent
man/hominid
earth/terrace
farming/agriculture
food/sustinence
dog/canine
cat/feline
horse/equine
cup/vessel or chalice
boss/supervisor
hearing/audition
seeing/vision
green/verdant
quick/expedited
mess/disorder
cut/excised
boyish/puerile
manly/virile
tree place/arboretum
house/domicile (Haus is German, Domus is Latin)
yearly/annual
womanly/feminine
motherhood/maternity <---- there's a store called "Motherhood Maternity" hahaha!
maidenhood/virginity
...and hundreds (thousands?) of others.