Using the example for Jack Reacher in your question, Skydance Productions is a production company under Paramount, otherwise known as a subsidiary of Paramount.
From Wikipedia, the production company...:
may be directly responsible for fundraising for the production or may
accomplish this through a parent company, partner, or private
investor. It handles budgeting, scheduling, scripting, the supply with
talent and resources, the organization of staff, the production
itself, post-production, distribution, and marketing.1 Production
companies are often either owned or under contract with a media
conglomerate, film studio, entertainment company, or Motion Picture
Company, who act as the production company's partner or parent
company. This has become known as the "studio system". They can also
be mainstream independent (see Lucasfilms) or completely independent
(see Lionsgate). In the case of TV, a TV production company would
serve under a television network. Production companies can work
together in co-productions.
Another example of a production company would be Blue Sky Studios, which produced such films as the Ice Age series, Rio, and Horton Hears A Who. They've been owned by 20th Century Fox since 1997.
A production studio that's a subsidiary of a larger studio may specialize in producing certain types of films. In the case of Blue Sky Studios, they've exclusively produced CG animated films for 20th Century Fox. However, Fox also has Fox Searchlight, which specializes in independent and foreign/foreign language films (they're the US distributor for 12 Years A Slave). Others are more independent, like Twisted Pictures, best known for the Saw franchise. They've released films with the help of both Lionsgate and Universal.
So basically, the other studios you see listed are likely owned by the larger studio, but have their own managers and staff (usually freelancers) who handle the production of certain movies. The larger studio usually acts as the distributor. Think of it as a way for the larger entity to hand tasks off to others within the same company, and the production company is basically a "department" of the main company. The CEO of a company doesn't handle absolutely everything from the various departments, and instead hires/appoints others to handle those tasks, all reporting back to him in some way.
Here's a nifty list of production studios, listed as subsidiary, non-subsidiary, or defunct.
Long story short: welcome to the crazy world of the studio system.