How to get the difference (only additions) between two files in linux

diff and then grep for the edit type you want.

diff -u A1 A2 | grep -E "^\+"

A similar approach to https://stackoverflow.com/a/15385080/337172 but hopefully more understandable and easy to tweak:

diff \
  --new-line-format="%L" \
  --old-line-format="" \
  --unchanged-line-format="" \
  A1 A2

Most of the below is copied directly from @TomOnTime's serverfault answer here. At the bottom is an attempt that works on unsorted files, but the command sorts the files before giving the diff so in many cases it will not be what is desired. For well-formatted diffs of unsorted files, you might find the other answers more useful (thanks to @Fritz for pointing this out):

Show lines that only exist in file a: (i.e. what was deleted from a)

comm -23 a b

Show lines that only exist in file b: (i.e. what was added to b)

comm -13 a b

Show lines that only exist in one file or the other: (but not both)

comm -3 a b | sed 's/^\t//'

(Warning: If file a has lines that start with TAB, it (the first TAB) will be removed from the output.)

NOTE: Both files need to be sorted for "comm" to work properly. If they aren't already sorted, you should sort them:

sort <a >a.sorted
sort <b >b.sorted
comm -12 a.sorted b.sorted

If the files are extremely long, this may be quite a burden as it requires an extra copy and therefore twice as much disk space.

Edit: note that the command can be written more concisely using process substitution (thanks to @phk for the comment):

comm -12 <(sort < a) <(sort < b)

You can try this

diff --changed-group-format='%>' --unchanged-group-format='' A1 A2

The options are documented in man diff:

       --GTYPE-group-format=GFMT
              format GTYPE input groups with GFMT

and:

       LTYPE is 'old', 'new', or 'unchanged'.
              GTYPE is LTYPE or 'changed'.

and:

              GFMT (only) may contain:

       %<     lines from FILE1

       %>     lines from FILE2

       [...]