In 1611, in the KJV, what did the words "ghost" and "spirit" mean?

They seem to have been used interchangeably, with some overlapping definitions and figurative usage in the English language before and leading up to the 17th Century translation of the KJV. The meaning of each is, at least in the Greek, dictated by context. Thus, each of these words for the translators in English also had multiple meanings and connotations that were rooted in the context in which they appeared in the text.

In regards to "Spirit,” “Ghost” (and “Breath”) in the New Testament Greek

It seems that the KJV translators viewed one definition of "spirit" as synonymous with "ghost," and that "breath" is sometimes used figuratively as a synonym of "spirit," much as the Latin word for breath, spiritus, was used figuratively to refer to the soul or spirit of a human being.

English Word Origins:

Spirit. Middle English: from Anglo-Norman French, from Latin spiritus ‘breath, spirit,’ from spirare (‘breathe.’)

Ghost. Old English gāst (in the sense ‘spirit, soul’), of Germanic origin; related to Dutch geest and German geist. The gh- spelling occurs first in Caxton (c. 1422 – c. 1491), probably influenced by Flemish gheest. (Oxford Dictionaries)

In Luke 24:37, when Jesus appears to the disciples, they are afraid because they think He's a ghost in the sense that we use the word today - a nebulous apparition of a dead person:

37 But they were terrified, and afrighted, and supposed that they had seene a spirit. (1611 KJV).

In this instance, the Greek word used is pneuma, which the translators rendered as "spirit." The context of the situation makes it clear what Luke meant by pneuma. Thus, we can take one of the definitions of "spirit" in the 1611 King James to be a synonym of our current English definition or meaning for "ghost."

As Jesus dies on the cross in Luke 23:46, we see pneuma again, and once again rendered by the 1611 KJV as "spirit" in English, but in the sense that we define "soul" today (the spiritual part of a person that gives life to the body):

46 And when Iesus had cried with a loud voice, he said, Father, into thy hands I commend my spirit: And hauing said thus, he gaue vp the ghost.

Again, the context of the usage makes it clear what Luke means by pneuma here. It's also interesting to note that "gave up the ghost" is the translators' rendering of exepneusen, or "he breathed his last." So we see "ghost" used as part of an idiomatic rendering of what appears to be an idiom in the Greek.

So, Why The Different Renderings?

As for why the KJV translators chose to vary the rendering with synonyms, we can look to the instructions and guidelines they were given by King James I. Whenever we discuss the King James, we must recognize the tradition of prior English Bibles and the influence they had on the language used in the KJV. As the translators of the KJV carried out their work, they were working under 15 “rules for revision” from the court of James I himself, most notably (in this case):

1. The Bishops' Bible (1602 revision) to be followed "and as little altered as the original will permit.”
2. Words of varying interpretations to be rendered in accordance with patristic tradition and the analogy of faith.
3. “These translations to be used when they agree better with the text than the Bishops' Bible: namely, Tindal's, Matthew's, Coverdale's, Whitchurch's, the Geneva.” (Pope, Hugh. English Versions of the Bible (Westport, Ct.: Greenwood Press, Publishers), pp. 309-325).

Therefore, we have to recognize that some words may have been maintained (especially where multiple interpretations are possible) according to the tradition established by English Bibles prior to the publishing of the KJV. In fact, the KJV’s wording lines up to be quite similar to The Bishops’ Bible on many counts. Returning to the example of Luke 24:37 from above:

37 But they were abaffled and afrayde, & supposed that they had seene a spirite. (1568 Bishops’ Bible)

It’s likely that words with multiple synonyms were kept the same as they were rendered in the Bishops’ Bible when the KJV translators were deciding on the final word choice for the King James. This wasn’t seen as something that would “muddy the waters,” but that would maintain the language tradition that had been established in prior English translations.