Why do VHS tapes degrade in two different ways when copied?
This is a difficult question to accurately answer; because you haven't detailed out the exact setup of how the tapes are being duplicated. 

First, VHS is an Analog format, and the video signal is typically output via a composite connection. Some higher end VHS consumer units did have component out, either by RGB or via S-Video Out. This connector would yield a higher quality transmission from your feed deck vs your record deck. 

So signal loss plays a big factor, especially if the decks are connected via composite (co-axial) connection, as all color information, along with luminance information, is on the same channel. 

Using S-Video at least separates out the Blue and Red Values; and pairs luminance with Green. 

Quality of the decks comes into play. Are we talking consumer decks; or professional Sony Editing/Duplicating decks. In their hey-day, The Sony Editing Decks, which were the size of about 3 normal VCRs tall, and 1.5 times as wide; were highly accurate in terms of carriage speed for the tape. The highest end decks were nearly frame accurate. They allowed pre-roll, where the decks would back up the tape, get the tape up to speed, and then insert edit in the record at the correct designated frame. 

Lastly; if the decks are not synced, there will be slippage regardless... It's analog not digital. 

The only way to maintain that both decks sync frame for frame is via genlock. The unit most popular during the Pro-VHS days was called a "Kitchen Sync", it was basically a black burst generator that had a bunch of outputs that all of your decks (they made different size syncs); would connect to, and all the decks would keep in sync with the master clock. 

Without that; it's impossible. 

Finally; VHS over time stretches, becomes brittle, there's different quality tape, it's magnetic, so it's susceptible to loss of information based off magnetic contact. 

Cheers!