Holy Spirit = Holy Ghost
Holy Ghost = Holy Spirit
In the Greek and Hebrew there’s no distinction whatsoever. Ruach in Hebrew, Pneuma in Greek. It is only in the peculiar funniness that is the English tongue where we run into a semantic difference.
Let’s look at a German translation of Isaiah 11:2 to help us out here.
auf welchem wird ruhen der Geist des HERRN, der Geist der Weisheit und des Verstandes, der Geist des Rates und der Stärke, der Geist der Erkenntnis und der Furcht des HERRN.
See there, German Geist? That’s the German cognate with English “ghost”, and it is being used to translate the Hebrew ruach.
Let’ look at how the Vulgate translates Isaiah 11:2
Et requiescet super eum spiritus Domini: spiritus sapientiae et intellectus, spiritus consilii et fortitudinis, spiritus scientiae et pietatis;
See here that same Hebrew word, ruach, is translated into Latin spiritus.
So let’s look at various English translations,
John Wycliffe’s 14th century translation was made using the Vulgate, and so Isaiah 11:2 in the Wycliffe Bible looks like this:
And the Spirit of the Lord schal reste on hym, the spirit of wisdom and of vndurstondyng, the spirit of counsel and of strengthe, the spirit of kunnyng and of pitee;
We see this also in later English translations such as the Coverdale:
The sprete of the LORDE shal light vpon it: the sprete of wysdome, and vnderstondinge: the sprete of councel, and strength: ye sprete of knowlege, and of the feare of God:
The first 1611 publishing of the KJV
And the Spirit of the Lord shall rest vpon him, the spirit of wisedome and vnderstanding, the spirit of counsell and might, the spirit of knowledge, and of the feare of the Lord:
All of this is post-Norman English, Wycliffe is Middle English, the English that emerged following the Norman Conquest, distinct from pre-Norman Old English (aka Anglo-Saxon), and later Early Modern English (Coverdale, the KJV, etc). Where the influence of Latin via Norman French is very much in full effect in English; and so English translations are using the Latin-based “spirit”, rather than the Germanic-based “ghost”.
When we look at other Germanic language Bibles, such as the German language Luther Bible I quoted earlier, we see geist, “ghost”. This runs true if we look at other Germanic language Bible translations,
Here’s Isaiah 11:2 in a Dutch translation:
De Geest van de Heer zal op Hem zijn. Hij zal vol zijn van de Geest van wijsheid, de Geest van verstand, de Geest van raad, de Geest van sterkte, de Geest van kennis van God en de Geest van ontzag voor God.
Again we see geest, “ghost”.
And we see this also in Flemish translations such as here:
En op Hem zal de Geest des HEEREN rusten, de Geest der wijsheid en des verstands, de Geest des raads en der sterkte, de Geest der kennis en der vreze des HEEREN.
And the language most closely related to English, Frisian, we see
De geest van de HEER zal op hem rusten: een geest van wijsheid en inzicht, een geest van kracht en verstandig beleid, een geest van kennis en ontzag voor de HEER.
Spirit/spiritus, ghost/geest/geist/gast. All are translating the same Hebrew word: ruach.
So Holy Ghost and Holy Spirit really is just a semantic case because of the peculiar funniness of English and the history of the English language. The meaning is identical: the Holy Spirit/Ghost is the Third Person of the Holy Trinity.
So we can confess in the Creed that “We believe in the Holy Ghost” (a more traditional translation) or that “We believe in the Holy Spirit” (a more modern translation) and it means exactly the same thing. The Latin of the Apostles’ Creed* says “Credo in Spiritum Sanctum”. So again, “Holy Ghost” or “Holy Spirit” is just semantics, the meaning is 100% identical.
*And if we look at the Greek of the Nicene Creed, we’ll see Pneuma; and again English translations either say “Holy Spirit” or “Holy Ghost” largely based on when the translation is made, older translations use “Holy Ghost” more modern ones use “Holy Spirit”. This is a common trend in English translations of Scripture, Christian prayers, the Creeds, and Christian texts of all sorts generally.