Is epiretinal membrane the same thing as macular pucker?

Yes: Yes, both terms describe the same condition. This condition results from a membrane forming from a remnant of vitreous that stays adherent to the retina after the vitreous separates from the retina. This condition may never cause visual issues, but in some people the membrane will wrinkle and may need to be surgically removed.

Yes: Another term for this is a wrinkle. They are often used interchangeably to describe a condition where a membrane grows over the retina. It often occurs spontaneously, and can remain stable or grow over time. Treatment is directed at peeling the membrane off the retina, and is usually not offered unless vision decreases below a certain level (20/50 or worse, depending on the surgeon).

Yes and no: The macula is the central part of the retina that gives us our ability to read and see fine detail. Epiretinal membranes tend to grow over the macula, contract and thus wrinkle our macula. This produces a wrinle in the macula that "puckers" it. Hence the term "macular pucker." surgery can remove epiretinal membranes and reduce symptoms in advanced cases.

Same: They both describe a thin layer of scar tissue which covers the macula and causes visual distortion.

Yes: Those terms mean the same thing. Additionally, sometimes a pucker is referred to as "scar tissue on the retina", and "epiretinal gliosis." when appropriate, surgery to remove the pucker may be a good idea to halt vision deterioration, or modestly improve vision. Best to see a retina specialist for this kind of problem.