Intel will be using the same lithography for sub Intel 7 geometries as TSMC has been using for their 3-7nm. They are not as far behind as you think. Lithography is the technology (ie EUV) used for patterning step of fabricating. Transitioning to EUV is basically mandatory to keep improving density. All major fabs have basically moved to EUV for sub 7nm geos.
For the record, Intel 7 has a smaller fin pitch than TSMC 7 even though its channel length (where traditionally transistors get their sizes) is longer. Intel 7 is also comparable in density as TSMC 7 because the fin pitch is less. Kind of why they call it Intel 7. It used to be their Superfin 10, but recent improvements too it makes it their 7. Its just kind of bad perf/watt.
Basically, saying something is Xnm doesnt mean shit these days due to transistor structures being very different than they used to be and largely marketting now. Transistors can be the same size from say TSMC 7 to TSMC 6, but to make it TSMC 6 they just say its density is improved, perf/watt is better, area better but transistors themselves didnt change. There could even be another flavor of cell that has different VT characteristics added to the library.