My previous dog loved to chase our cat. He'd be lying on the couch, and` she would walk up to him and start poking him with her snout to try to get him to run. He would either stay put or slowly slink away.
My first dog would make this happy grunting noise when she saw someone she knew.
My cat Noodle has a petting spot - one very specific area of the living room floor where she allows pets to happen. When we’re playing and she senses that pets are imminent, she will dart over to the petting spot and flop over on her side. Petting may now commence.
Also, she has developed the habit of jumping on top of me in the middle of the night and licking my nose. I haven’t decided if she’s bored and wants attention or if she’s checking to see if I’m dead so she can start eating me.