A recent full diplomatic relation restoration between the US and Cuba took place, does that mean that US citizens can go to Cuba freely and vice versa?
No, travel is still not completely free. However, you are now allowed to travel to Cuba and spend money there legally under the following 12 categories:
- family visits
- official business of the U.S. government, foreign governments, and certain intergovernmental organizations
- journalistic activity
- professional research and professional meetings
- educational activities
- religious activities
- public performances, clinics, workshops, athletic and other competitions, and exhibitions
- support for the Cuban people
- humanitarian projects
- activities of private foundations or research or educational institutes
- exportation, importation, or transmission of information or information materials
- certain export transactions that may be considered for authorization under existing regulations and guidelines.
Note the absence of plain old "tourism" from this list. In practice, though, it was already pretty easy to visit Cuba legally under the fig leaf of "people-to-people exchanges", and with these wide new categories, it's about to get even easier. (A week of dancing salsa or tasting cigars? Sounds "educational" to me!) You will still likely need to go through a travel agent unless sorting out licenses with the Office of Foreign Assets Control sounds like your idea of a good time.
Strictly speaking, US law does not completely forbid travel to Cuba. There are even organized tours.
The main restriction impairing free travel to Cuba is the embargo which prohibits US citizens to conduct business or any monetary transactions with Cuban interests. Since this embargo was established by a series of statutes, the president cannot overturn that without the help of the US Congress and it's unlikely to happen soon.
At the same time, there is a system of licenses authorizing people to spend money in Cuba to allow travel for limited purposes. Apparently, the current US presidency intends on facilitating that process so even if travel still won't be completely free, it could become easier.