In my opinion these are two different dimensions. You have the delivery method: SaaS vs. self-managed/on-premises. And you have the license of the code: proprietary vs. open-core (which can be fully open source, open-core, or a non-compete license like the one MongoDB and CockroachDB switched to).
At GitLab we have an open-core license and offer the product both as SaaS and self-managed, so we do both things in the title. The opposite would be companies offering only proprietary software that you run yourself, like Sketch.
Another dimension would be billing, people frequently mention SaaS as an example of subscription billing. At Gitlab we also bill for our self-managed software on a subscription basis instead of a big license fee upfront and yearly maintenance.