My older 14-3 wire is thicker then the newer 14-3 wire can I use the new with the old:confused:

Are you looking at the gauge of the copper of the overall thickness including insulation? 14 gauge is 14 gauge, hasn't changed and handles 15 amps quite well.

Newer NM cable is MUCH thinner than the old stuff. Especially if the old stuff has TW insulated conductors and the paper packing inside.

The newer outer sheath and the THHN conductors inside are much thinner.
Same cable though.

Side question: So what about the grounding conductor, was that always the same size conductor in older cable?

Yep, all 3 wires were the same gauge but the insulation has changed a lot.

Much older NM cable, like from the 50's, had a much smaller ground wire. This cable was used extensively, but it didn't last a long time.

Much older NM cable, like from the 50's, had a much smaller ground wire. This cable was used extensively, but it didn't last a long time.
Exactly! I see it all the time...