Elon Musk revealed his plans for SpaceX to go to Mars in September of 2016. It involves the building of the Interplanetary Transport System and he plans to launch the first humans to Mars in 2024.
NASA’s Mars plan is far more involved with investigating the problems of long-term interplanetary flight, as they plan to build space stations in ciclunar orbit over the course of 14 years, the Deep Space Gateway and the Deep Space Transport, which will become the planetary vessel they will use for the first manned mission to Mars in 2033.
NASA’s plans revolve around the new Orion capsule, which is the first manned spacecraft NASA has created since the Space Shuttle. It is meant for deep-space travel and habitation. Meanwhile, SpaceX plans to launch the manned version of their Dragon capsule, the Dragon 2, in 2018, which will open up more opportunities for the private space company.