Technically speaking, is there a difference between the Biblical terms "other sheep" and "great crowd"?
Yes, though we should not be unduly sensitive about word usage or be upset if someone uses the terms interchangeably.
Most Christians are familiar with the passages where we find these terms. John 10:16 is one. There Jesus said: "I have other sheep, which are not of this fold; those also I must bring, and they will listen to my voice, and they will become one flock, one shepherd." The other expression, "great crowd," appears at Revelation 7:9. We read: "After these things I saw, and, look! a great crowd, which no man was able to number, out of all nations and tribes and peoples and tongues, standing before the throne and before the Lamb, dressed in white robes; and there were palm branches in their hands."
Let us consider John 10:16 first. Who are the sheep? Well, it would be good to fix in mind that all of Jesus loyal followers are referred to as sheep. At Luke 12:32, he called those of his disciples who would be going to heaven the "little flock." A flock of what? Of sheep. The "sheep" of the "little flock" will be part of the Kingdom in heaven. However, there are others, those with a different hope, whom Jesus also views as sheep.
We can see this in John chapter 10. After speaking about sheep such as his apostles whom he would call to life in heaven, Jesus added in verse 16: "I have other sheep, which are not of this fold; those also I must bring." Jehovahs Witnesses have long recognized that in this verse Jesus was speaking of people having the prospect of life on earth. Many faithful ones in pre-Christian times, such as Abraham, Sarah, Noah, and Malachi, had such prospects. So we can rightly include them as part of the "other sheep" of John 10:16. During the Millennium, such faithful pre-Christian witnesses will be resurrected and will then learn of and accept Christ Jesus, becoming "other sheep" of the Fine Shepherd.
We also know that since the general call of the heavenly class ended, millions have become true Christians. These too are rightly termed "other sheep," since they are not part of the "little flock." Rather, the other sheep today look forward to living right on into an earthly paradise.
Now, what can be said about the identity of the "great crowd" mentioned at Revelation 7:9? Well, look at verse 13 and the question, "Who are they and where did they come from?" We find the answer at Revelation 7:14: "These are the ones that come out of the great tribulation." So the "great crowd" is composed of those who come out of, or survive, the great tribulation. As verse 17 says, they will be guided to fountains of waters of life on earth.
Understandably, though, for these to survive the approaching great tribulation, they must earlier have washed their robes in the blood of the Lamb, becoming true worshipers. Hence, though Revelation 7:9 is describing this crowd after the tribulation, we may apply the term "great crowd" to all with earthly hopes who are rendering Jehovah sacred service now, just before the great tribulation breaks out with the nations attack on false religion.
In summary, we might remember "other sheep" as the broader term, encompassing all of Gods servants having the hope of living forever on earth. It includes the more limited category of sheeplike ones today who are being gathered as a "great crowd" with the hope of living right through the impending great tribulation. Most of those loyal Christians alive today are of the "other sheep," and they are part of the "great crowd" as well.
It is worth repeating that, fine as it is to be clear on these specifics, there is no need for any Christian to be overly word conscious - what might be called word critical. Paul warned about some who were "puffed up with pride" and involved in "debates about words." (1 Timothy 6:4) If we personally recognize certain distinctions between terms, fine. Yet, we need not, either outwardly or inwardly, be critical of another who may not use Biblical terms quite as precisely.
Although JWs do speak of themselves as being part of the "great crowd", on the Publishers Record Card one is either "Anointed" or "OS".