Intel's 7nm is likely closer to TSMC's 5nm than their 7nm but Intel will be stuck on 14nm while AMD is on 7nm for quite awhile.
This is why they are delayed. Intel always lagged in density over TSMC. TSMC's 32/28nm generation was a mere 30% larger than Intel's 22nm process. It really didn't matter though, because Intel got theirs 1-1.5 years ahead of TSMC and it performed better which was good for Intel's bread-and-butter business.
So they wanted to catch up, and really
catch all. So they said we'll get it 1.5 years earlier, have better density even at the same generation, all the while having the best performing transistors.
That's why 14nm got seriously delayed. Everyone forgot about the delays to 14nm, even though that was significant, because 10nm dwarfs 14nm in how bad the situation is. Sure, 14nm is small, but you got it delayed by 6 months, and only Atom cores benefit, so who the heck cares?
Then they doubled down on this density e-peen with 10nm. "We'll make 10nm dense as the next generation TSMC, while retaining performance" they said.
They became too overconfident, and lost sight with reality. Nothing to do with engineering and technology. Just egotistic and short-sighted thinkers. Kinda like genius teenagers. Yea they are smart in a category, but can they adult?