The following are terms that you may come across if you do much solving of LP's using packages. If one or more of these variables is zero then the basis is degenerate. Obviously the ideal situation is when moving from one vertex to another we improve the objective function value by a significant amount. The worse case is when the objective function value is unchanged when we move from one vertex to another. The revised simplex algorithm is one example of a primal simplex algorithm.
Many packages contain both primal and dual simplex algorithms.
Trying dual simplex is particularly useful if your LP appears to be highly degenerate. At a minor iteration no inversion is done. The algorithm stops when the optimal solution is found. There are also more sophisticated tests available that enable reduction in the size of the LP to be achieved. Generally preprocessing is a good idea as it can reduce LP solution time dramatically.