Different voltage panels are primarily just the number of series connected cells in a panel.
There is about 0.65v Voc and 0.54v Vmp per cell at room temp. Voltage goes down at about -2.1mV/degC per cell as panel heats up so you will generally not get the advertised room temp voltages spec in actual use when sun heats up panel.
Not really a difference on shading. Any partial shading will take out a section of cells common to one bypass diode. Bypass diodes are really for safety reasons to avoid having too much reverse bias voltage across a single cell during shading which could make it get very hot. Usually less then 20 series connected cells per bypass diode to keep reverse voltage less then about 12 volts. Usually there are an even number of long rows of cells in a panel and a bypass diode is put across each down and back long row pair. This allows the connections be brought out to junction box on one end of panel where bypass diodes are placed. If a panel has six long rows of cells there will be three bypass diodes in panel.
A 72 series cells panel is common for higher power panels with a Voc of 72 x 0.65v = 46.8v.
36, 60, and 72 series cells per panel are common. There are some low cost '12v' panels with 32 or 33 cells per panel. This low number of series connected cells may not work with an MPPT controller on a 12v battery, as a single or paralleled panels, as they have an Vmp too low to operate an MPPT controller which require 4v to 6v of overhead voltage above battery voltage to operate properly. They are lower power panel typically bought for low cost system using a PWM controller. You can use the low cell count panels with MPPT controller if panels put in series to get higher voltage, however, beware some of these 32 or 33 cell panels have only one or no bypass diodes. If they do not have any bypass diode and you stack them you can get into trouble during shading.
Some manufacturers are using half cut cells to get more yield out of their cell wafer stock. They may put two half cells in parallel or series connect half cells. You might see a panel listing 144 cells. They would be half cells and Voc would be like a 72 cell panel as two match graded half cells are paralleled making them act as one full sized cell. Standard wafer size is 156mm x 156 mm and puts out about 8.5 to 9 amps at full sun intensity.
