There is a huge difference; it has to do with how to understand a control problem. The traditional form of optimal control is located within the number crunching domain. A control statement is used to influence a system with a mathematical value. For example we can feed the number “-1” into the plant and get a certain result as a consequence. The result depends on the nonlinear differential equation which describes the inner working of the system.
In contrast, the term action is used in more recent publications which are trying to abstract from the mathematical control theory in favor of a linguistic description of a problem. Action based reinforcement learning is strongly connected to natural language parsing. An action primitive isn't a mathematical value like “-1” but it's a grounded statement like “move left”. The hope is, that linguistic grounded actions have a better modeling performance for complicated systems.
In most cases, actions aren't feed into a mathematical equation but into a grammar driven model. An action like “moveleft” has much to do with language parsing, but only little with a classical pid control problem. Actions are used for solving complex problems, while control signals are useful for non- compound tasks.