I'll try and clear up any confusion you might have about GitLab. Feel free to ask more questions if I left something out.
> I can't find anything describing the relationship between GitLab and Git anywhere on the home page.
The relation between git and GitLab is that GitLab is a front-end for git. However, it's so much more than that. We strive to offer features that encompass the whole DevOps lifecycle - see https://about.gitlab.com/direction/#scope for more context.
We have an integrated CI/CD system, issue tracker with boards and epics, built-in container registry, monitoring and many many others. All of them are listed in https://about.gitlab.com/features/
> Likewise, I honestly can't tell whether GitLab is an OSS project or some sort of hosted enterprise "call us for pricing" behemoth
GitLab Community Edition (CE) is a completely open-source project - https://gitlab.com/gitlab-org/gitlab-ce . It's MIT licensed.
We offer a proprietary version with added features - GitLab Enterprise Edition (EE) - https://gitlab.com/gitlab-org/gitlab-ee . It has a proprietary license. Even though it's proprietary, Enterprise Edition is source-visible i.e. you can browse the source.
> There's a pricing page with various plans including a free plan, but while I initially assumed they were for a hosted online service, apparently they're for self-hosted.
There's both a hosted solution (GitLab.com) and the option of self-hosting. The pricing page has two tabs - one for self-hosted options and the other for GitLab.com
> There is information about many ways to install GitLab locally on different platforms, but it's not clear what you're actually installing at that point or whether you then need some sort of licence to do anything with it.
No matter which package of GitLab (Community Edition or Enterprise Edition) you install locally, you'll always be able to access the free tier of features without a license.
> On the features page, each item has two different scales under it, one for GitLab and one for GitLab.com, but I really have no idea what the relationship between those is.
There's four feature / pricing tiers for self-hosted instances: Core (Free), Starter, Premium and Ultimate. From left to right, every tier has more features than the previous one. The distribution of features is documented in https://about.gitlab.com/features/ (upper scale).
If you opt for a hosted solution on GitLab.com, there's also 4 pricing / feature tiers: Free, Bronze, Silver and Gold. All public projects have access to Gold-tier features for free. The feature distribution between these tiers is also documented in https://about.gitlab.com/features/ (lower scale).
> There is an entirely separate feature comparison table that is actually linked from the pricing page, but that only shows one of the scales, and suggests that the lower/free tier is quite restrictive.
We prioritize features for one of the paid tiers if we think the feature is more relevant for larger organizations.
You can find out more about our stewardship of the open-source GitLab CE project at: https://about.gitlab.com/stewardship/