what is the difference between O(nk) and O(n+k) in time complexity?

Question

In big O notation of time complexity in algorithmic analysis, when an algorithm depends on n and k, what is the difference between these two notations. Also pls help in the notation to use if there is a nested loop with outer loop running n times and inner loop running k times ?

Answer 1

O(nk):

for( i=0; i<n; i++ ) {
   for( j=0; j<k; j++ )
   {}
}

O(n+k):

for( i=0; i<n; i++ )
{}

for( j=0; j<k; j++ )
{}