Whats the difference between reversible process in thermodynamics and reversible chemical reactions?
There is no misunderstanding at all.

The second law of thermodynamics can be roughly expressed as: in a given process the entropy of the universe will always increase (defining universe as system + surroundings). 

Reversible processes

For reversible processes the entropy of the universe remains constant. Most natural occurring processes are irreversibles.

A reversible process is a process where you can change its direction by inducing infinitesimal changes to the system. Throughout the entire process the system is at equilibrium, so from one state A to a state B you will not observe macroscopic changes.

The system goes from state A to state B in the following way: A + dA = B where B is infinitesimally different from A. These changes are applied over properties of the system like temperature and pressure by modifying its surroundings.

Reversible chemical reaction

In the case of a reversible chemical reaction it means that if you combine the products of that reaction you’ll obtain at least some of the reactants again. Usually these reactions require the same amount of energy that was consumed or released to obtain the products (This means that you must take into account the enthalpy of the forward reaction). 

A typical example are lead batteries where lead reacts with sulfuric acid to form lead sulfate and $\ce{H+}$ ions while the battery is discharging and then you apply a direct current to revert the reaction and obtain lead, sulfuric acid and lead oxide again.

Even when a reaction is thermodynamically possible you must take into account the kinetics parameters. For example: it is thermodynamically possible to turn graphite into diamond but kinetically at standard conditions (1 atm, 25$^\circ$C) it will happen in millions of years.