Junzuki, a front punch.
Gyakuzuki, a reverse punch
Maegeri, a front kick.

Kette Junzuki, front kick stepping forward front punch
Kette Gyakuzuki, front kick stepping through with a reverse punch.

What I want to know is, where does the kette part of the name come from?

Kette seams to mainly be used only in Wado. there is the same topic on another forum here:

http://www.all-karate.com/forums/index.php?showtopic=2520

Why is this term mainly used in Wado. I must admit i've never heard it before...

What would be a similar term in other styles of karate?

it is probably only used in Wado because Ohtsuka created the translation. The same thing exists in all schools, the head instructor from one school calls a lunge punch.. a lunge punch, another a leading punch, another a front punch, another a jab punch. so then all students from call it as per their teachers translation. There are mainy ways to decribe the same technique, what students tend to forget is that it is only a 'description' not a name. If you want to name a technique you should call it some thing like 'zuki1', 'the terminator' or maybe just 'bob'.