AC mains rectifier issue
The \$\sqrt{2}\$ relationship between RMS and peak voltages only holds for perfect sine waves. Your meter is a typical average-of-absolute reading meter with an 11.1% span shift to make it pretend to read RMS with sine waves. 

The readings you are getting are more an indication that your mains power is somewhat distorted. It's not unusual to have the tops of sine waves flattened by circuits like those you are building (but drawing substantial power) unless they incorporate power factor correction, because they only draw power near the peak of of the waveform. 

You should be seeing about 310VDC if the sine waves were perfect and you are seeing 293, that's not a huge difference, a bit over 5%. It's also on the low side, corresponding to the flattening I mentioned. 

Similarly, the difference between measurements indicates that your mains voltage waveform is probably changing a bit.

See, for example, this answer which has actual mains waveforms from a US lab. 


  Both this and the household mains show a peak voltage that's lower than what we'd expect for a pure sine wave with the measured RMS value.




Your meter (when measuring AC mains) is measuring the average |voltage| and scaling it so it approximates RMS for a sine wave. When measuring the DC across the capacitor, after the bridge, it's measuring the peak voltage (minus diode drops), approximately. 

For a perfect sine wave and no diode drops the ratio of Vpeak/Vrms is \$\sqrt{2}\$.

If the tops of the sine waves are flattened off, the peak voltage is decreased more than the average or RMS voltage of each half cycle. Think of it approaching a square wave where a true RMS meter would read 1.00 for Vpeak/Vrms rather than about 1.414. It will also slightly affect the reading on your meter on the AC range, which will tend to read higher than the actual RMS value. A square wave would read 11.1% higher value than true RMS on a meter like  yours. Those two factors add, so the measured peak voltage is less than expected from the apparent RMS value.

If you make the mains measurement with a true-RMS reading meter, you should see a bit less of a difference. Hopefully that's intuitive if you think about what RMS really means.