I'm taught that:
Ayumiashi is a "normal" step, for example you advance from hidarihanmi to migihanmi;
Okuriashi is a "side" step - you make two steps, not changing the hanmi;
Tsugiashi is a "small" step, you don't change the hanmi stance while making "tsugi-ashi";
Tenkaiashi is "turning around" - you make "tsugiashi", look backwards, then turn your hips;
Tenkan'ashi is "turning around with one step backwards" - you make a "tenkai-ashi" then "ayumi-ashi" backwards;
Irimi tenkan is "tenkan'ashi" after "ayumi-ashi".
in Aikido Tankyu #17, p.28 (Irimi), Doshu says that you enter with "Okuri ashi" (when UKE ends his attack in Gyaku-hanmi).
The way Simon wrote.
In another dojo I saw Okuriashi (what I mean about Okuriashi) called "Ayumi-ashi".
And so on.
I've also heard the word "Suriashi" or "Shuriashi" (I'm not sure which one is the correct one)