The two-story gray platforms at the base were originally built for Apollo, modded for shuttle, and now modded again for SLS.
The towers are new and suffered a lot of cost and schedule issues. Most of the Apollo towers were scrapped, but some remnants of them were used to build the fixed service structures for Shuttle. One of those was subsequently modded for use by SpaceX.
SLS MLP-1 started as LUT-3 for Apollo. It was used for five crewed Apollo Saturn V launches and 50 shuttle launches.
SLS MLP-2 started as LUT-2 for Apollo. It was used for one uncrewed and three crewed Saturn V Apollo launches and for the launch of Skylab. It was used for 49 shuttle launches.
Normally Saturn 1s were launched from Complexes 34 and 37 and didn't use MLPs. But the Skylab and Apollo-Soyuz crews did use the MLP with the famous "milkstool" for their launches. This was MLP-3 which started as LUT-1 and was used for one unmanned and two manned Saturn V launches as well. It was used for the remaining 36 shuttle launches.
Note: The Wikipedia and wiki numbers for MLP usage on shuttle launches are obviously wrong since they don't add up to 135. I have used the data from the Shuttle Almanac.
Personal note: if you've ever been in a WW2 museum battleship, that's exactly what going into the MLP interior smells and looks like.