Solved the old fashion way. Even though I used only Windows - along the years there were many problems like this one. Thought posting this can add to your knowledge of how to help someone with a similar problem, in the future.
I unplugged Puppy's drive; deleted TC's partition with Gparted from Puppy's live-CD (before that - I formatted; which I saw that leaves some of the disk space "used"; so it doesn't really format it I guess); formatted to ext4; installed TC with the option "Mark Partition Active (bootable)"; the computer booted into TC's boot options; after plugging Puppy's drive - with F8 I can boot into Puppy. Tried a few times to make sure I can boot into both OS's.
Yeah, usually starting over is easier than rummaging through the settings etc.
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