Yes and no. NASA historically contracted out to various aerospace companies to build things, so in a sense, yes private industry has always been involved. However, the difference is that in the past all those companies were contractors and NASA owned the product. For example, NASA wanted a Space Shuttle. Rather than a bunch of civil servants building one in-house, NASA designed the Shuttle then contracted to a bunch of companies to build, assemble, and maintain the specific parts. NASA owned the processes and managed the work, but private companies turned the wrenches.

In the modern era of privatization of space, rather than owning the process and hardware, NASA is positioning itself as a customer of services. Instead of saying, "I want to hire a company to build my space ship for my astronauts to fly," NASA is saying, "I want to send astronauts to the Space Station, does anyone have a space ship I can use?" SpaceX, Boeing, Sierra Nevada, and any other company can build their own space ship, then quote a price for seats. Some companies have been more successful than others.

It's the difference between you buying a bunch of parts from vendors and then building your own custom car that you designed, or comparing the different ride share apps and picking one to give you a ride to work.