omp parallel vs. omp parallel for

There are obviously plenty of answers, but this one answers it very nicely (with source)

#pragma omp for only delegates portions of the loop for different threads in the current team. A team is the group of threads executing the program. At program start, the team consists only of a single member: the master thread that runs the program.

To create a new team of threads, you need to specify the parallel keyword. It can be specified in the surrounding context:

#pragma omp parallel
{
   #pragma omp for
   for(int n = 0; n < 10; ++n)
   printf(" %d", n);
}

and:

What are: parallel, for and a team

The difference between parallel, parallel for and for is as follows:

A team is the group of threads that execute currently. At the program beginning, the team consists of a single thread. A parallel construct splits the current thread into a new team of threads for the duration of the next block/statement, after which the team merges back into one. for divides the work of the for-loop among the threads of the current team.

It does not create threads, it only divides the work amongst the threads of the currently executing team. parallel for is a shorthand for two commands at once: parallel and for. Parallel creates a new team, and for splits that team to handle different portions of the loop. If your program never contains a parallel construct, there is never more than one thread; the master thread that starts the program and runs it, as in non-threading programs.

https://bisqwit.iki.fi/story/howto/openmp/

TL;DR: The only difference is that the 1st code calls 2 implicit barriers whereas the 2nd only 1.

A more detail answer using as reference the modern official OpenMP 5.1 standard.

The OpenMP clause:

#pragma omp parallel

creates a parallel region with a team of threads, where each thread will execute the entire block of code that the parallel region encloses.

From the OpenMP 5.1 one can read a more formal description :

When a thread encounters a parallel construct, a team of threads is created to execute the parallel region (..). The thread that encountered the parallel construct becomes the primary thread of the new team, with a thread number of zero for the duration of the new parallel region. All threads in the new team, including the primary thread, execute the region. Once the team is created, the number of threads in the team remains constant for the duration of that parallel region.

The:

#pragma omp parallel for 

creates a parallel region (as described before), and to the threads of that region the iterations of the loop that it encloses will be assigned, using the default chunk size and schedule (which is typically static). Bear in mind, however, that those defaults might differ among different concrete implementation of the OpenMP standard.

From the OpenMP 5.1 you can read a more formal description :

The worksharing-loop construct specifies that the iterations of one or more associated loops will be executed in parallel by threads in the team in the context of their implicit tasks. The iterations are distributed across threads that already exist in the team that is executing the parallel region to which the worksharing-loop region binds.

Moreover,

The parallel loop construct is a shortcut for specifying a parallel construct containing a loop construct with one or more associated loops and no other statements.

Or informally, #pragma omp parallel for is a combination of the constructor #pragma omp parallel with #pragma omp for.

For both versions that you have shown if one uses chunk_size=1 and static schedule the execution flow would result in something like:

Code-wise the loop would be transformed to something logically similar to:

for(int i=omp_get_thread_num(); i < n; i+=omp_get_num_threads())
{  
    //...
}

where omp_get_thread_num()

The omp_get_thread_num routine returns the thread number, within the current team, of the calling thread.

and omp_get_num_threads()

Returns the number of threads in the current team. In a sequential section of the program omp_get_num_threads returns 1.

or in other words, for(int i = THREAD_ID; i < n; i += TOTAL_THREADS). With THREAD_ID ranging from 0 to TOTAL_THREADS - 1, and TOTAL_THREADS representing the total number of threads of the team created on the parallel region.