Both are Linux so many the same.
Tiny Core by default uses busybox and therefore command options may differ.
Tiny Core by defaul uses ash shell and not bash.
Both of the above can be replaced by their GNU counterpart extensions.
All the Debian package management commands are not in Tiny Core.
Tiny Core uses Appbrowser, Appsaudit, and corresponding command line: ab, tce-load, tce-audit
Fundamentally Debian is a traditional hard drive installed system. Tiny Core,by way of recommendation is, ram based OS with mounted application extensions.