appserver is one of two types:
thin and thick. if the client is thin, then the server  can do all the processing
in some cases, and results are sent to the client. for instance, telnet, all
work is done at the server end.

however, thin client can be a client without a hard drive, and the 'appserver'
serves the binarys.

web server, potentially has thin clients. for jsp  though, some work is done on
the client, such as reproduction of the plain text that is sent to the client in
the form of a document image (with exception to binarys (gif/jpg/swf)).

it does not matter if your answer is right or wrong, they asked  that question  to
test your understanding of the two components. if you cant tell the difference
between two common terms like app/webserver then you probably cant do the job.
appserver is not comonly used like webserver  these days as many clients are
meaty 32bit processors, thus there is little point trying to save money on
processor requirements and buying a central mainframe because of cheapness of
processors.

in theory the app server has been replaced by the webserver as many apps are run
on webservers now.

although i have not done much jsp, i believe that some work is done on the
client side.

web server, potentially has only thin clients, before you ask i would not class
javascript as part of the work involved in producing a webpage as javascript is
optional, unlike the work which must always be done by php/asp/jsp.