We read of a horn that is small at first, but it is not the same as the one from Daniel 7! The little horn that we encounter in Daniel 7 does not appear until after the fourth world empire that follows the Greek-Macedonian Empire; it comes only after the fourth realm, the Roman Empire, loses its power. It does not appear until all kinds of other kingdoms have come into being.
The little horn we read about in Daniel 8 comes from one part of the third empire, the Greek Empire. It is notable, however, that it is also called a small horn. If you read further, you see that in the behaviour of this small horn there is already the aura of the Antichrist (the small horn of Daniel 7). It is a smaller representation of the Antichrist which will later plague the church with fearful power.
23 And at the latter end of their kingdom, when the transgressors have reached their limit, a king of bold face, one who understands riddles, shall arise.