It's the same picture. These days, God's standards for morality often come under attack for being out of date or too narrow. Like the false teachers of whom Peter wrote, people who think this way only bring destruction unto themselves. If words are easy, try putting love into action. Do the dishes, take out the trash, change the oil, clean the cat box.
Love has lots of definitions.
Your life needs to be different from the lives of those who don't have the Holy Spirit living within them. The picture in this passage is of a new heaven and a new earth where God and his people will live forever together. Every child eventually has questions about heaven. Answer your children truthfully, but not with more information than can be found in the Bible.