What are the practical differences between amillennialism and historical premillennialism?

Among the different eschatological schemes in Christian theology, I perceive that amillennialism and historical premillennialism do not differ in what they believe will happen before the second coming of Christ. (Or at least, they do not have to. I know that there exist some disagreements about futurist vs. preterist understandings of Matt. 24 or about the gathering of Israel in Rom. 11, but it does not seem to be the case that the interpretations of these passages separate premillennialist from amillennialist in general.) Postmillennialism and dispensational premillennialism on the other hand differ from one another and the aforementioned views in that they assert a different timeline of pre-Second Coming events, with postmillennialism looking forward to a millennium of the triumphant church and dispensationalism looking forward to a pre-tribulational rapture (and a very different understanding of that tribulation than would be found in other views). I am wondering what difference does the distinction between historical premillennialism and amillennialism make, practically speaking? Does it have any effect on how Christians will conduct themselves in the present age? I can see that, if we look forward to different events *prior* to Christ's return, this may affect the way we live our lives now, in order that we might be prepared to face those circumstances. However, I do not see how the difference between historical premillennialists and amillennialists who agree on those issues would lead to any different practice of the faith in the present time.