Gravity goes down during cooling

Really the only thing that would account for a .010+ variance is that the first sample was concentrated with more sugars than the second. Temperature cannot account for such + to - swing with any gravity meter. A hydrometer would read less gravity at hotter temps since the hotter water is expanded and has more volume and less density, objects floating in them have less buoyancy causing a hydrometer to read lower than actual SG when at proper temp.

In simple terms the wort was not fully mixed during the first sample and was more evenly mixed at the second sample.

One other alternative, check your cooler for leaks!

If you've accidentally diluted the wort, it'll have a lower gravity.

How did you measure the gravity? Hydrometer or refractometer?

What temperature did you measure at post-boil? What temperature did you measure at post-chill?

The change in gravity is expected. Your gravity measurements need to be calibrated for temperature. You can use https://www.brewersfriend.com/hydrometer-temp/ to do this or have a paper copy of a calibration table on hand.

Also, if you are measuring gravity post-boil with a glass hydrometer, be careful! I can shatter due to high temperatures or temperature shock!

Measurement at different temperature can cause this.

Use this site to adjust the measurement depending on the temperature: https://www.brewersfriend.com/hydrometer-temp/

Sedimentation can also change the value a little, but that would take some time.