Something to note is that the key to irimi of the kind pictured above is the "C" back which is central to the internal arts (and aikido, for that matter). However, the opposite is true in the "ura irimi shown by Tim Cartmell here at 0:22 to 0:25: http://www.youtube.com/watch?v=OuP6cApKAD8
(ura irimi is the "inverted" version of normal irimi).
Chofukainoa - what you wrote was very interesting:
In motobu udundi, my sensei has always just called it "ayumi" or walking, along with the other walking techniques. Our really basic one is one diagonal step to enter, one continuing step to unbalance, and then a step at 90 degrees to take down or throw.
My internal Chinese martial arts applies the same principle - take a look at the diagonal steps etc. in the links to the forms under my picture of irimi (ayumi) above.
The name "ayumi" literally means, as you have said, "walking" (eg. "ayumi ashi" is the normal step, as opposed to, say, "suri ashi" or sliding step). It is for this reason that I prefer "irimi" to describe the concept of "entering" another's space - it is more specific. Otherwise you are correct in the sense that it is a "walking" movement.
I'd absolutely love to see/train in motobu udundi, btw. It seems like a fascinating art - right up my alley, so to speak.
Eyrie - you said:
There's a reason for all those "wrist manipulations" in Aikido... and equally so for those unrealistic "wrist grabs"... it's all about irimi... enter and walk thru...
While I agree with the thrust of your comment, I don't think that wrist grabs are quite so unrealistic as people will popularly say nowadays. If you look at our sparring video http://www.youtube.com/watch?v=2tL9rGeKZGU you'll see lots of wrist grabs applied offensively (to trap, control, throw, etc.). If they are applied offensively then you can use escapes against them defensively. I'm not sure if there are in any in the video, but I apply kote gaeshi, for example, routinely in fast free sparring. I think the reason you don't see grabs in free fighting is the same reason you don't see deflections: People might train them as basics, but never apply them on the floor.
In my experience, you can't do a form or basics and expect the techniques to magically appear in your sparring... That is why we have methods to transition from one to the other (randori, embu - our 2 person forms, etc.).