Hormonal terms Somatotrophin or somatotropin?
Yes

They are the same thing, and both are old-fashioned terms for what is now termed specifically growth hormone (i.e. not generically as in "a growth hormone"). It is clear from the Wikipedia entry for growth hormone that this is equivalent to somatotropin. 

I could not find a specific scientific reference that states that the two are the same, but I present a line of reasoning based on a search for mention of the terms in books using the Google ngram.



The initial similarity in the curves in the left-hand frame reflects, I think the competing use of the terms when the hormone activity was first discovered. Eventually somatotropin won, although the use of growth hormone is much more common now (right-hand frame).

If you look at the books cited by the ngram in which somatotrophin is used, you will find that many are in the field of animal science, especially dairy science in relation to the lactogenic effect of the hormone. Years ago I worked in this area, and remember that growth hormone had such lactogenic effects.  Presumably somatotrophin stuck in this area, whereas somatotropin was more generally used, especially in human endocrinology.

General Dictionaries and possible reasons for variation

I am hesitant to quote non-scientific dictionaries on scientific topics, but in this case it is probably justified, and it also addresses the difference in meaning of ‘tropin’ and ‘trophin’, referred to in the question.

The Merriam-Webster online definition of somatotrophin redirects to:


  somatotropin
  variants: or less commonly somatotrophin


Chambers on-line only has somatotrophin, But my own 1994 printed edition has:


  somatotropin or somatotrophin a polypeptide growth hormone


My Chambers Dictionary iPhone app also has both.

And Saunders Comprehensive Veterinary Dictionary, 3rd ed. (2007), according to a citation in the Free Medical Dictionary, has:


  somatotropin, somatotrophin
  growth hormone


If you check the meanings of the two suffixes in Merriam-Webster:


  -trophic
  of, relating to, or characterized by (such) nutrition


Whereas


  -tropic
  1 : turning, changing, or tending to turn or change in a (specified) manner or in response to a (specified) stimulus
  2 : attracted to or acting upon (something specified) 


It seems probable, therefore, that the original form was somatotrophin, but, either by confusion with the second definition of -tropic or a North American chemical aversion to ‘ph’ (as in sulphur/sulfur), somatotropin became dominant, except in the field of animal science. Perhaps that is why the Oxford Dictionary, both online and in my printed edition of 1991, ignores somatotropin completely. However you would have difficulty ordering somatotrophin from the chemical supplier, Sigma-Aldrich/Merck, whereas somatotropin is available.