Same general direction perhaps but the all around space between all these objects is expanding at a high rate of speed as well.
I guess what I'm trying to say is the lateral distance is increasing as well. So, to simplify it... If you had two objects going in the same general direction (i.e.- That Way), the distance between the two would increase even though they continued going generally 'that way'.
I guess, think about two highways that start at the same place and run roughly parallel at first and are headed in seemingly the same direction. If you were driving in a car on one highway and your neighbors were driving in a car on the other one and you were both driving the same speed, for a while it would probably not even seem like you were moving in relation to one another.
But if the 'side by side' distance between those two highways increased by only a little bit per mile, after a while you would be able to note that the other car was moving still towards the west coast (for example) but more and more away from you and your family (laterally). If this continued eventually the other car would be far off in the distance, even though still moving generally west. They could even be doing the same speed as you to start with but as this lateral disparity in distance increased, you would note an acceleration away from your own position. This would give you the red shift.
You see what I mean?
That's roughly a two dimensional model. With an explosion or the Big Bang, you would have that phenomenom happening in 3 dimensions.
Now, I realize this begs the question- what about people driving on the same highway with you? ;-) But think about this- in the three dimensions plus Time of a rapidly expanding space/universe- those cars travelling on the exact same path as you would only represent one very tiny point in the heavens (if you would find it at all). Even very tiny disparities in trajectory would add up very quickly and produce the red shift. Given several billion years it would become very marked indeed, thus you would measure a red shift in everything you saw.
That's the way I see it anyway.