Difference between ingress and service's kubernetes session affinity

Question

What are the differences between using an nginx ingress with the session affinity annotations (as below example) and a service with the service.spec.sessionAffinity set to ClientIP.

From what I understand, both reach the same goal but I wonder if there are some differences other than the primer being done at ingress level with a cookie while second operates at the service level using the clients IP. Also, would that be a bad idea to use both a the same time ?

And last question, If I want to enable sticky session between pods within the cluster, would the service.spec.sessionAffinity: ClientIP definition would be enough to ensure a backend pod connects everytime to the same database pod ?

Ingress example :

apiVersion: networking.k8s.io/v1
kind: Ingress
metadata:
  annotations:
    kubernetes.io/ingress.class: nginx
    nginx.ingress.kubernetes.io/rewrite-target: /
    nginx.ingress.kubernetes.io/affinity: cookie
    nginx.ingress.kubernetes.io/affinity-mode: persistent
    nginx.ingress.kubernetes.io/session-cookie-change-on-failure: "true"
    nginx.ingress.kubernetes.io/session-cookie-expires: "172800"
    nginx.ingress.kubernetes.io/session-cookie-max-age: "172800"
    nginx.ingress.kubernetes.io/session-cookie-name: STICKY_SESSION
    nginx.ingress.kubernetes.io/use-regex: "false"

From the Kubernetes' service API documentation :

sessionAffinity : Supports "ClientIP" and "None". Used to maintain session affinity. Enable client IP based session affinity. Must be ClientIP or None. Defaults to None. More info: https://kubernetes.io/docs/concepts/services-networking/service/#virtual-ips-and-service-proxies