In essence, the Cluster API harmonizes how to get to clusters, while Gardener goes one step further and also harmonizes the clusters themselves. The Cluster API delegates the specifics to so-called providers for infrastructures or control planes via specific CR(D)s while Gardener only has one cluster CR(D). Different Cluster API providers, e.g. for AWS, Azure, GCP, etc. give you vastly different Kubernetes clusters. In contrast, Gardener gives you the exact same clusters with the exact same K8s version, operating system, control plane configuration like for API server or kubelet, add-ons like overlay network, HPA/VPA, DNS and certificate controllers, ingress and network policy controllers, control plane monitoring and logging stacks, down to the behavior of update procedures, auto-scaling, self-healing, etc. on all supported infrastructures. These homogeneous clusters are an essential goal for Gardener as its main purpose is to simplify operations for teams that need to develop and ship software on Kubernetes clusters on a plethora of infrastructures (a.k.a. multi-cloud).
Incidentally, Gardener influenced the Machine API in the Cluster API with its Machine Controller Manager and was the first to adopt it, see also joint SIG Cluster Lifecycle KubeCon talk where @hardikdr from our Gardener team in India spoke.
That means, we follow the Cluster API with great interest and are active members. It was completely overhauled from v1alpha1 to v1alpha2. But because v1alpha2 made too many assumptions about the bring-up of masters and was enforcing master machine operations (see here: “As of v1alpha2, Machine-Based is the only control plane type that Cluster API supports”), services that managed their control planes differently like GKE or Gardener couldn't adopt it (e.g. Google only supports v1alpha1). In 2020 v1alpha3 was introduced and made it possible (again) to integrate managed services like GKE or Gardener. The mapping from the Gardener API to the Cluster API is mostly syntactic.
To wrap it up, while the Cluster API knows about clusters, it doesn't know about their make-up. With Gardener, we wanted to go beyond that and harmonize the make-up of the clusters themselves and make them homogeneous across all supported infrastructures. Gardener can therefore deliver homogeneous clusters with exactly the same configuration and behavior on all infrastructures (see also Gardener's coverage in the official conformance test grid).
With Cluster API v1alpha3 and the support for declarative control plane management, it became now possible (again) to enable Kubernetes managed services like GKE or Gardener. We would be more than happy, if the community would be interested, to contribute a Gardener control plane provider.