Are soft boiled eggs and poached eggs identical? Today I heard from a friend, that poached eggs are simply glorified soft-boiled eggs and that there is no way to distinguish between the two except for the form. The only reason anyone does poached eggs is because soft-boiled eggs are kind of hard to peel.

He then told me that you can make a hole in an egg, soft boil it, than because of the small hole you can peel it easily basically eliminating the main disadvantage of soft-boiled eggs: difficulty when peeling.

The result is supposed to be identical to a poached egg.

I have had both soft-boiled eggs and poached eggs many times, and I always felt that poached eggs have a unique taste and texture.

Or is the hole in the egg mimicking the poaching because it lets water in?

You are supposed to make the hole on the flatter side of the egg, where the air pocket is.
I'll answer the question in your title.  Poached eggs are eggs, removed from the shell when raw, and cooked in a liquid.  The consistency of the yolk can vary depending on the poaching time. The consistency of the white is generally the same each time. Poaching usually happens at a temperature below the boil.

Soft (or medium, or hard) boiled eggs are eggs that are left in the shell, but cooked in boiling water. The assumption in the comments, that the cooking is stopped before heat reaches the yolk, in not correct.  Soft boiled eggs can certainly have yolks of varying consistency, it is just that they are not hard.  The white, is of course, protected by the shell to some degree, so the consistency can vary depending on the cooking time.  It is often more done near the shell, and of a looser consistency as it approaches the yolk.

Egg yolks and whites are very sensitive to cooking time and temperature, so small variations produce different results.  In addition, the yolk and white behave differently.  It is why many have found cooking eggs sous vide so interesting. 

So, yes, the processes produce different results and should not be considered the same.