With updates to some versions, you can just replace tinycore.gz and bzImage.
With updates to other versions, other files are also changed.
As mentioned, check the release notes with each version, to see what files, if any, are changed.
If you are not sure, another option is to delete personal settings when you update.
Save a copy of all files you don't want to lose from /home/tc.
If you use persistent home, delete /home/tc.
If you use persistent /opt, delete /opt.
If you use backup, delete mydata.tgz (normally in the tce directory).
After doing this, when you start the new version of Tiny Core, it will be the same as a new installation.