敬語 consists of 尊敬語, 謙譲語 and 美化語.
お as a prefix can be either 尊敬語, 美化語 or neither.
The concepts of 尊敬語 and 美化語 are mutually exclusive, but お can be either 尊敬語 or 美化語. For example,
お/ご as a 尊敬語: お名前, お着物, お住まい, おビール, ご婦人, ご来店, ごゆっくり
(Can be only used to refer to something that belongs to your boss, etc)
お/ご as a 美化語: お箸, お菓子, お風呂, お片付け, ご禁制, ご大層
山田孝雄, a Japanese linguist, called this type of phrase/sentence 喚体句. This is used to make a sentence sound dramatic and vivid. It is especially common in poetry (haiku, lyrics, ...), but this pattern is often seen in live commentary in sports and in the narrative part of novels, too. He called ordinary sentences (ending with a verb/adjective/copula) 述体句. ...
First, wasei eigo should be viewed as a subcategory of eigo-gairaigo, i.e. gairaigo derived from English.
So, the pattern should look as follows
wasei eigo ⊂ eigo-gairaigo ⊂ gairaigo
Gairaigo are words taken from foreign languages in general, and eigo-gairaigo are words derived from English; lastly wasei eigo is literally English made in Japan (i.e. words ...
外科 is more commonly used to refer to the field of surgery academically and professionally, and is a noun. 手術 is more used to refer to the act of surgery and can be a verb.
In other words, if the former is thought of as "surgery," the second can be thought of as "operating" or "an operation."
I think I can see how you are confused about these two words, but I feel like the confusion might have stemmed from the English Japanese dictionary definitions, or rather the confusing nature of the English word "surgery". I don't think the two Japanese words overlap as much as the related English concepts.
"Surgery" is a medical ...