The idea is that Chapter 7 indicates the rise of the anti-christ from out of the 10 horns which arise out of the area of the old Roman Empire. Thus the little horn of Daniel 7 is the Anti-christ. Daniel 8 gives a description of Antiochus who so terribly persecuted Israel and who is also used as an example of the type of abomination that the anti-christ brings. Part of this involves something some call a "gap Theory" which means that there is historical application then end time application. As we know there is nothing in the Old Testament that really indicated a long period of separation between the first Advent of Jesus Christ and the Second Advent of Christ. In prophetic terms, they are seen as one event. So there really is no way to get around using the "gap theory". Even the SDA version uses it though they don't really acknowledge it. For instance the SDA theory holds the Papacy as the anti-christ from 538-1798 then at some point they expect the anti-christ to arise and cause even more prosecution. So really there is not as much difference between the theories. As the SDA theory expects the rise of Anti-christ in the future as do the other Christian denominations.
The following site gives a pretty good description of the way I see these chapters. It is not a very long article but hits most of the important points. Antiochus IV Epiphanes: The Antichrist of the Old Testament By Larry Cockerham
Antiochus IV Epiphanes was the eighth in a succession of twenty-six kings who ruled from 175—164 BC over the Syrian section of Alexander’s empire. He is referred to as the “little horn” in Daniel 8:9. The name Epiphanes means the “Illustrious One,” although his contemporaries nicknamed him Epimanes, meaning “madman.”1 He differs in many respects with the “little horn” of Daniel Chapter seven seeing that “the little horn of 7:8 appears in the context of the fourth kingdom (Rome), while the little horn of 8:9 appears in the context of the third kingdom (Greece).”2 Yet taken as a whole Antiochus IV Epiphanes is undoubtedly one of the greatest prototypes of the Antichrist in all of God’s Word.
The prophecies of Antiochus Epiphanes in Daniel (Dan. 8:9-14; 23-25; 11:21-35) have both a historical as well as future fulfillment. Because these prophecies point both to Antiochus Epiphanes as well as the future Antichrist of the New Testament Bible students call them a double reference prophecy. However, liberal commentators, such as D.S. Russell, see in these verses only a historical fulfillment due to their late dating of the Book of Daniel (165 B.C.).3 Conservative scholars, on the other hand, realize both a historical completion (they were still future when Daniel wrote them) in Antiochus as well as future prophecies that prefigure the Antichrist. There are also differences of opinion among fundamental Bible scholars as to where the prophecies regarding Antiochus end and those pertaining to the Antichrist begin. We will at this time focus on the comparisons or parallels between the wicked Syrian king Antiochus IV who viciously and cruelly persecuted the Old Testament saints of God and the coming “man of sin” commonly referred to in the New Testament as the Antichrist.
(1) Both involve two end-time periods. When it comes to the larger picture, these two periods of persecution leading up to the first and second coming of Christ are portrayed in both the exploits of Antiochus IV as well as those of the coming Antichrist. Lehman Strauss explains thusly:Both of these periods witness the wrath of God being extended to His chosen people. The first of these periods of wrath commenced with the Babylonian captivity and concluded with the atrocities of Antiochus, after which there was deliverance. The second of these periods is yet future. It will commence with the beginning of the seventieth week (Daniel 9:24-27) and conclude with the atrocities of Antichrist, after which there will be deliverance.4
Therefore not only is there a typical relationship between the two persons of Antiochus IV Epiphanes and the upcoming Man Of Sin, but there is also an association between the two time periods leading up to the end of each era.