There are a couple things that Forrest and I want to point out (Forrest is traveling today and asked me to jump online).
The Lexus wheel is what we'd simply call a coated wheel -- coated with a silver paint, and certainly clearcoated (at least the factory spec would likely have been). It appears to have been refinished as indicated by some peeling of silver paint. Refinishing is often done during a "certified used" process, but the quality varies greatly depending on brand of vehicle. It can also be done at the dealer or owner level. With a refinished wheel, the durability is often not on par with OEM specs. A strong cleaner may clean a bit too well on a finish that is not up to standards, and either may stain that finish or possibly even cause a bit more peeling. This peeling we see here will certainly get worse over time regardless of any wheel cleaner being used.
The Cadillac wheel is what is often called a "polished aluminum" wheel, and it is factory coated (all OEM "polished aluminum" wheels are coated with a clear). As Forrest mentioned, it appears to have lost some clearcoat which is exposing bare aluminum (though it could be bad water spotting). Addressing missing clearcoat gets a little tricky as the bare aluminum will oxidize and may need polishing with a metal polish like our Mag & Aluminum Polish. It also has some corrosion under the clearcoat as indicated by those bumpy spider-veiny areas, and those will require sanding (which will remove the clearcoat) and a multi-step finishing and polishing process.
While in their current condition, a wheel cleaner really won't benefit the wheels, though both wheels look like they could stand some general finish polishing to bring up the luster. A great multipurpose product like our California Gold Scratch Remover should remove any light scratches and oxidation (even on the bare alloy; use a metal polish if it doesn't). Follow with a good wax, like our California Gold Synthetic Wax for protection.
All too often we don't care for our wheels as we should. Routine washing and waxing is a great way to prevent conditions like we see here, though years and miles eventually catch up to any wheel. I like to recommend using a spray wax as you dry on the body panels, but also finish with the door jambs and finally the wheels.
If you need a wheel cleaner, use it; if you don't, don't.
If you have specialty wheels with a matte finish, exotic finish (like anodized), or if you have brake components with such finishes, use car wash to avoid problems. Even though these were originally glossy finishes and our Foaming Wheel & Tire Cleaner would have provided excellent results when these wheels were newer, in their present condition that could prove to be an error.
So again, the 06024 Polished Aluminum Wheel Cleaner would be a better choice if you do need a wheel cleaner -- but as shown here, they really aren't dirty.
Let us know if you need more assistance or clarification.