Diane Bondareff/hard Rock International/AP
Melissa Etheridge had already been raising two children, so she was no novice parent when her twins were born
But the new additions, she tells PEOPLE, have turned out to be "a whole different ball of wax."
"They have their own language, they are more content to be with each other. With twins, it's like you're in their life," she says of her 11-month-old son Miller Steven and daughter Johnnie Rose.
Etheridge, 46, and partner Tammy Lynn Etheridge, 32, conceived the twins via artificial insemination, and Tammy carried the babies. Melissa also has two children from a previous relationship with Julie Cypher: daughter Bailey Jean, 10, and son Beckett, 8.
Speaking before a concert at Hard Rock Cafe New York on Tuesday – to kick off a breast cancer awareness campaign called "Rocktober" and to launch her new album The Awakening
– Etheridge says that although she already had a boy and a girl, the twins made evident inherent gender differences.
"I used to think it was society but no, no, no," she says, laughing. "You can put the same thing in front of both of (the twins) and they will do completely different things. He will see if he can break it, if he can throw it, and she is going to contemplate it, see how she can manipulate it."
Plus, with twins, she says, "Even their relationship to each parent is different because they have a relationship with each other at first."
Etheridge, diagnosed with breast cancer in 2004, says her health now is excellent. Her head, made bald by chemotherapy, is now covered with blonde, shoulder-length hair.
"It's an interesting experience to walk through life and have people burst into tears," says Etheridge. "The experience of breast cancer, or cancer in general, everybody knows somebody who has had cancer, it's always there. Everybody has that story."