Are soft boiled eggs and poached eggs identical?
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.