What is the difference between critical summary and appreciation?
To best answer your question, one must first define the terms for which you are asking.
The word "critical", according to Dictionary.com, means:
involving skillful judgment as to truth, merit, etc.
The word "summary", as given by Google, means:
A brief statement or account of the main points of something.
Therefore, a critical summary finds truth and/or merit as applied to an account of something in regards to the main points.
Appreciation is defined (according to Google) as:
The recognition and enjoyment of the good qualities of someone or something.
This being said, one can blatantly see the differences between the two. For one to partake in a critical summary of a work, they must provide a summary of the text , paying special attention to the main points and details, while using "skillful judgement". An appreciation is much different. One only needs to like something based simply upon the good qualities they find in the text. One does not need to use "skillful judgment" to justify an appreciation. Appreciations do not typically need to be justified.