What gets copied (and what doesn't) during a Target Mode copy?

I recently cloned my old, dying computer into a new one, using Target Mode and a Firewire 800 cable via Recovery Mode. Everything looked perfectly identical. I launched Safari on the new computer, and all the tabs I was browsing were there. But when I opened Chrome, there were no tabs open, and the extensions were uninstalled. I'm trying to understand what happened, and where these files were copied for Target Mode to omit them.

Which files does Target Mode copy - and which files does it not copy - when cloning a hard drive with Recovery Mode?

Target Disk Mode just turns the whole Mac into an external drive. There's essentially no difference between doing that and taking the drive out and putting it in a FireWire drive enclosure.

There's nothing special about TDM that makes it not-copy certain files.

However, when using a cloning app, some files may or may not be included. These are usually just 'temporary' data, such as caches, or machine-specific files that the system will recreate if absent. There may be options in the cloning app to exclude other files.