Another (python) option, offering a bit of a "fancy" report:
----------------------------------------------------------
Newly copied from /home/jacob/map 1 to /home/jacob/map 2:
- Naamloos document
- pscript_2.py
- test123
- monkey_out.txt
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Unique files in /home/jacob/map 2:
- file_in_targetfolder
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It does what you describe:
- it copies files from folder A to B if they do not (yet) exist in B
- reports files in B, which are not in A
The script
#!/usr/bin/env python3
import sys
import os
import shutil
folder_1 = sys.argv[1]; folder_2 = sys.argv[2]
files_1 = os.listdir(folder_1); files_2 = os.listdir(folder_2)
# make the length (n) of separating line "smart"
s = "\nNewly copied from "+folder_1+" to "+folder_2+':'; n = len(s)
print("\n"+n*"-"+s)
for f in files_1:
    f1 = folder_1+"/"+f
    if all([os.path.isfile(f1), not f in files_2]):
        shutil.copyfile(f1, folder_2+"/"+f)
        print("-",f)
print(n*"-"+"\nUnique files in "+folder_2+":")
for f in files_2:
    f2 = folder_2+"/"+f
    if all([os.path.isfile(f2), not f in files_1]):
        print("-",f)
print(n*"-")
How to set up
- Copy the script into an empty file, save it as - sync_report.py
 
- Test- run it by the command: - python3 /path/to/sync_report.py <folder_a> <folder_b>
 - If the directories contain spaces, put them between single quotes. 
- If all works fine, use it as above, or: - 
- make the script executable
- add the following command to a shortcut key: - gnome-terminal -e "'/path/to/sync_report.py' '/path/to/folder_a' '/path/to/folder_b'"
 - Choose: System Settings > "Keyboard" > "Shortcuts" > "Custom Shortcuts". Click the "+" and add the command. 
 - Then, when the key combination is pressed:  
 - Don't let the background distract you, my terminal is semi-transparent. :) 
Alternatively, as mentioned by @ParanoidPanda (thanks for mentioning), add it to your ~/.bashrc file. Create an alias which calls the script:
alias <nameofalias>='python3 /path/to/sync_report.py <folder_a> <folder_b>'