Compare two files line by line and generate the difference in another file

diff(1) is not the answer, but comm(1) is.

NAME
       comm - compare two sorted files line by line

SYNOPSIS
       comm [OPTION]... FILE1 FILE2

...

       -1     suppress lines unique to FILE1

       -2     suppress lines unique to FILE2

       -3     suppress lines that appear in both files

So

comm -2 -3 file1 file2 > file3

The input files must be sorted. If they are not, sort them first. This can be done with a temporary file, or...

comm -2 -3 <(sort file1) <(sort file2) > file3

provided that your shell supports process substitution (bash does).

The Unix utility diff is meant for exactly this purpose.

$ diff -u file1 file2 > file3

See the manual and the Internet for options, different output formats, etc.

Consider this:
file a.txt:

abcd
efgh

file b.txt:

abcd

You can find the difference with:

diff -a --suppress-common-lines -y a.txt b.txt

The output will be:

efgh 

You can redirict the output in an output file (c.txt) using:

diff -a --suppress-common-lines -y a.txt b.txt > c.txt

This will answer your question:

"...which contains the lines in file1 which are not present in file2."