In reality, work can be converted to heat entirely but not vice versa. This is in accordance with second law of thermodynamics. So, no process is possible in practice where heat is entirely converted to work.

Take for example the heat engine. It has to reject some heat to the sink and convert the remainder into work. Thus, entire heat supplied is not converted into work. On the other hand, in a refrigerator, work has to be supplied to transfer heat from a colder body to hotter surroundings-in this case, the entire work input is converted to heat.

In practice, reversible isothermal processes are impossible because heat transfer always takes place across a finite temperature difference. This is an irreversibility. Thus, the entropy of the system will always increase if there is a heat transfer to the system. In that case, the amount of heat supplied to the system cannot entirely be converted to work (unlike reversible isothermal processes where heat is entirely converted to work).

So, both the statements are clearly true but the second one does not explain the first one.