Contrary to what some people think, cats are quite capable of displaying extreme affection.
I have three that will sit on my feet if I am standing and they want attention, sometimes rolling over and wallowing around on their backs.
One is a sweet 12 year old boy that is usually asking for a belly rub
...and one a big, sweet 4 year old girl who asks to be picked up and then flips over in my arms to be held like a baby, purring and nuzzling.
The other is a new member- 9 month old kitten.
I also have an old (at least 9 years that we know) boy that will tap with his paw until you pet him.
One of the other new girls is starting do do this some times.
But it al boils down to the individual cat. They are unique, and all have different traits.