Not unless you have home network storage and are saving it there.

I use. Evernote for all my notes and reference material.   It syncs with my iPad and computer.  It also has a web client so I can pull it up on any computer.   If you dropped your image in and hit sync you could open it on the other system.   It will also sync automatically.  You might need copy it out and back in after each edit.   




evernote.com

If you keep both computers in the same local network, you could use just about any sync tool that exists out there. I used SyncToy by Microsoft for quite a while (www.microsoft.com/en-us/downlo…), and it is really just as easy as setting up the folders you want to sync, and the tool synchronizes the files in both folders. Your advantage here compared to cloud storages like dropbox would be, you don't need a high speed internet connection to transfer a 200MB Photoshop file to your cloud storage and then download it again to your other computer

You can have a single external hard drive on which you would keep your work. Just plug it into whichever computer you are using.
That way both computers would see the same image, and mods done with one would be seen by the other.
I distrust the cloud. There is a potential for other people to access anything online.

Yup Drop Box, or if you wanted a different solution you can also use a Networked Shared drive and you can work off that directly. It would be quicker then drop box but requires purchases hardware.

You could also use a computer mirroring software (you control the actions of another computer)?
But that's sounds too cumbersome for what you want it sounds

Dropbox would do that (and also upload the files to your own personal dropbox site), but I would go with BitTorrent Sync, www.getsync.com/how-it-works (download here www.getsync.com/platforms/desk…) basically you install the BitTorrent program on your laptop and desktop, get the key and share it to the other computer, then set up a shared folder on both computers.  Any changes to a folder will be synced to the other computer, and unlike dropbox, there's no restrictions in terms of file sizes (since there's no cloud with BitTorrent Sync).

You can use programmes like dropbox for this. Dropbox is like a folder on your computer which you can put your files into, however once you put a new file in there, the file is synced to any other devices you have your dropbox folder installed on. It works the same for updating files as well, once you save the changes, it updates all the devices I think the cloud does something similar but I've only ever used dropbox. I hope that helps.