docker.io/library is the default registry applied when you don’t specify a registry URL.
When you specify -t in the build command, the text before the / is considered the registry URL.
Here is an example of building an image, one without a specific registry and one with:
# no registry specified
➜ docker build . -t my-image
[+] Building 0.5s (6/6) FINISHED
=> [internal] load build definition from Dockerfile 0.0s
=> => transferring dockerfile: 86B 0.0s
=> [internal] load .dockerignore 0.0s
=> => transferring context: 2B 0.0s
=> [internal] load metadata for docker.io/library/ubuntu:20.04 0.0s
=> CACHED [1/2] FROM docker.io/library/ubuntu:20.04 0.0s
=> [2/2] RUN cat /etc/lsb-release 0.4s
=> exporting to image 0.0s
=> => exporting layers 0.0s
=> => writing image sha256:4a97ceefb5314bdf91886a28142c9b0b33c992c94b1847d5ae1b38723b2279e3 0.0s
=> => naming to docker.io/library/my-image 0.0s
# registry set to "my.docker.registry"
➜ docker build . -t my.docker.registry/my-image
[+] Building 0.1s (6/6) FINISHED
=> [internal] load build definition from Dockerfile 0.0s
=> => transferring dockerfile: 36B 0.0s
=> [internal] load .dockerignore 0.0s
=> => transferring context: 2B 0.0s
=> [internal] load metadata for docker.io/library/ubuntu:20.04 0.0s
=> [1/2] FROM docker.io/library/ubuntu:20.04 0.0s
=> CACHED [2/2] RUN cat /etc/lsb-release 0.0s
=> exporting to image 0.0s
=> => exporting layers 0.0s
=> => writing image sha256:4a97ceefb5314bdf91886a28142c9b0b33c992c94b1847d5ae1b38723b2279e3 0.0s
=> => naming to my.docker.registry/my-image
The image tag specifies where the image will be uploaded if you do a docker image push <image name>.
In the first case, if you did docker image push my-image it would push to docker.io/library.
In the second case, if you did docker image push my.docker.registry/my-image it would push to a registry at the URL my.docker.registry (assuming it exists)