I think people are mistaking the word " renraku" (meaning to contact someone) with "renzoku" which means "continuous."
Saito Sensei once said that the term "Renzoku Waza" was a term used in Hombu Dojo, where in Iwama the term was "kanren (connected) Waza". Although the terms were different, they both were used when speaking about moving from one technique into another in a flowing form.
Now there are two versions of this practice, one of which could also be termed "Henka Waza" in my opinion. This would be when for instance you do shihonage and before you control uke after the throw, he comes back on his feet. Here you could segue into kotegaeshi with a hand change. This could be termed Henka Waza because you are changing or adapting to a new set of circumstances.
The "Kanren Waza" form of this same sequence would be where you take the initiative and give uke the opening to stand up again (uke should always revert back to a natural standing position when not being controlled by nage, the way I see it). When leaving uke the opening to stand up you blend with this movement and move into kotegaeshi before he regains his position completely. You can connect many techniques in this way, by leaving an opening for uke and then continuing into the next technique. Sometimes Saito Sensei would go from ikkyo through to rokkyo as Kanren Waza," for instance - leading uke all the way through the changes.
I also understand Henka Waza as being what has been described in other posts: using a variation of a given technique when in a situation where the basic form proves difficult to execute. This would mean a variation of the same technique that is more natural to perform when for instance uke changes his posture, grip etc.