Each of our cats shows their affection differently.
Jitzu is very standoffish with most people. I love how clingy she is with me, my SO calls her my familliar because she's always within 6 feet of me when I'm home. But my favorite thing that she does just for her mommy is purr. She never purrs for anyone else and I love that when shes especially happy to see me I can just barely hear her purr. For Jitzu that's absolutely amazing.
Torri shows her love by sleeping on top of me most nights. She purrs and snuggles, and kitten-rolls around until she just comfortable. She never sleeps on her daddy, but that's just because he moves more than me. I think the sweetest thing she does is insist that she have both of us in bed together before she goes to sleep. If only one of us is in our room in bed she stands at the door crying and yelling for her other parent to come to bed. It's loud, but sweet.
Doran...oh my silly momma's-boy. Doran is super clingy with me. If I'm sitting down he's next to me, or half on my shoulder/lap, or right up on top of me in my face. He drools, and purrs, and pushes his forehead to my mouth for kisses. I love all those things, but the bit that really melts my heart is when he goes to the vet. He puts his little furry arms around myu neck and hides his face under my chin for his shots. He doesn't cry or fuss, but he has to hug him mum to get needles. That's serious trust.
Muffin just loves everyone. Lately though he has been all over his dad (my SO). When my SO comes home Muffin is instantly all over him, rubbing on his face and legs and hands, purring up a storm, following him (purring) all over the house. It's so cute! He'll lie on my SO's legs while he's on the computer and just rub his face on my SO's stomach and legs for as long as my SO will let him. It's adorable!
I think very cat is unique and shows affection differently. If Jitzu started acting like Muffin I'd think someone drugged her!