jwilder/nginx-proxy has 1.3K STARS and 10M+ PULLS on Docker Hub. And Watch 262, Star 7701, Fork 1546 on GitHub. https://github.com/jwilder/nginx-proxy
kubernetes/ingress-nginx has 13 stars on kubeapps.com (one of the most starred charts) and Watch 137, Star 1596, Fork 918 on GitHub. https://github.com/kubernetes/ingress-nginx
In Kubernetes, the user decides what set of features to make public and in what manner configuration should be implemented. Help may come from enterprise vendors, like Ingress controller provided by GKE, and from community/private-held sides covering the uncommon approach to similar aspects of delivery services.
In this particular case, we have two nginx driven solutions.
An Ingress controller is full-featured and mostly recognized as default traffic controller to use with GKE.
Ingress can be configured to give services externally-reachable URLs, load balance traffic, terminate SSL, and offer name-based virtual hosting.
Users request ingress by POSTing the Ingress resource to the API server. An Ingress controller is responsible for fulfilling the Ingress, usually with a loadbalancer, though it may also configure your edge router or additional frontends to help handle the traffic in an HA manner. Nowadays Ingress is strictly cloud-oriented regarding configuration, it uses ConfigMap style and kubedns to register services.
If you know how old-fashioned virtual hosts work and you are not interested in every new cloud-oriented aspects of web services delivery, jwilder/nginx-proxy may be interesting for you. In this solution, nginx can act as a proxy to control internal hosting and world Web traffic with IPv6 ready endpoints. jwilder/nginx is not especially dedicated to clouds but also works fine there. If you are interested in having free Let's Encrypt certificates, there is an out-of-a-box support for it. Some users find it interesting that Basic Authentication is available, and the SSL is more flexible to configure for advanced purposed.
That is 2 different applications, but both are based on Nginx and have the similar function.
Nginx-proxy by jwilder is a proxy server for Docker containers which includes docker-gen to generate a configuration for Nginx automatically. You can use it for SSL termination, load balancing etc. But it will be hard to manage nginx-proxy in Kubernetes.
Ingress-nginx by Kubernetes is Ingress Controller which provides Ingress functional for your Kubernetes cluster. It also can do SSL termination and some other things, but it was created especially for use in Kubernetes, and it's abstractions. That means you can create the Ingress object which includes Services as backends and use selectors etc.
So, if you are using Kubernetes, Ingress-nginx is the best choice. If you are using just Docker containers without an orchestrator, use Nginx-proxy.