What is the difference between endergonic reactions and endothermic reactions? Exergonic and exothermic? The terms seem to be very similar, but not identical; is there a difference?

Endergonic and exergonic refer to free energy changes (delta G). Endothermic and exothermic refer to the changes in internal energy of molecules, measured as heat given off or taken up, delta H. Delta G takes into account not only changes in internal energy but also changes in entropy (delta S) that may accompany a reaction. For most ordinary simple chemical reactions, the entropy factor is not great, so chemists usually talk about delta H. For many biological reactions,the entropy factor is significant, so biochemists usually talk about delta G. Delta G = delta H - (T x delta S ). Despite the signs, which have to do with the way these terms are defined, delta G is the sum of the 2 effects. Becker presents this very nicely. You may forget about delta H for this course. More in a later lecture.