Here are some examples of different brand architectures, the primary difference being “branded house” (everything is endorsed by #1 or the corporate brand) or “house of brands” (each brand appears to be a standalone). Often it’s a mix of the two.
Companies use a “branded house” approach when they are very invested in the corporate brand but at the same time need a way to differentiate between the services the company offers. Here, GE.
When the brand name is different from the corporate name but has the corporate name somewhere in there it’s called an “endorsing brand” strategy. Endorsing brands are used to build up the credibility of various standalone brands while simultaneously explaining that each one does something different (e.g. is premium or low-end). Here, Marriott.
House of Brands
The “house of brands” strategy is typically used when the company wants to grow market share. Under a single brand umbrella they proliferate products. You think you have a choice, one company makes all the money. This is useful in the mass market because consumers tend to get bored and want new experiences.
In the government “brand wars” tend to erupt and become irrational for a few reasons.
1) Someone is trying to establish precedent, turf, policy or power and the brand legitimizes that effort.
2) There is a belief that a logo itself means that something has been achieved and so the more logos, the more achievements.
3) There is a desire to either unify or break apart an organization and the logo becomes a way of doing that (rather than having conversation/agreement first).