A git repository is usually only the
.git/ folder. But git repositories have -- in most cases -- a working directory, too. Only bare git repositories do not have a working directory, and those are only needed in special circumstances. When people talk about git repositories, its sometimes ambiguous if they only mean the
.git/ folder, or
.git/ folder and working directory. You will find, however, that this distinction is nearly meaningless in practice, since cloning a repo will also check out the working directory. And if some piece of software is tracked via git, changes in the working directory will be picked up by git. thus, there is little distinction between "the codebase" and "the repo", because both are more or less the same thing -- the codebase is in the working directory, which is intrinsically linked to the repo anyways.
A software repository and a source code repository are different things. A git repo or SVN repo are source code repos. They typically contain the source for one piece of software or one project, although its technically possible to shoehorn multiple pieces of software into the same repo.
A software repository on the other hand typically houses the artifacts of many software projects. Another term for a software repository is a registry, like the docker registry or npm registry. Maven repositories or the various repositories for Debian packages are two examples for such software repositories.
Nowadays, it becomes more and more popular to connect these repositories. For example, a change in the git repository might cause the CI/CD pipeline to run, which in turn will upload the built artifact to a software repo, and possibly also a ready-to-use docker container to a docker registry.
Services like GitLab and GutHub are taking on multiple roles. GitLab is primarily a hoster for git repos. Each git repo houses the source code for a piece of software. But they also offer package registries and docker registries where one can house their own artifacts. Similarly, GitHub also offers a container registry and a package registry. Those are mostly tied to the git repos hosted on those platforms, though, and not necessarily available for software hosted in other git repos.
Software repositoryis vague, but often refers to a package repository like NuGet or Maven. Git is specifically for storing source code.