Point taken. If I talk to "normal" people, I wouldn't use the word "protocol" neither (or at least not as conversation starter). Normal-people-rephrased it's more like
"When whatsapp take the fundamental core from signal..."
can Signal be used to contact people on Whatsapp?
As far as I know: no. Whatsapp just implemented the (open source) signal protocol formerly known as Axolotl with the help of Open Whisper Systems. The rest of the IM "ecosystem" (like push notifications, contact recognition, server infrastructure etc.) is left untouched.