All successful and attempted landings on Mars to date have used ablative heat shields. NASA shields have all been variants of phenolic impregnated carbon, sometimes with and oxide coating. The ESA missions have also used ablative heat shields although their composition is not publicly available. It's hard to find the details of Russian missions to Mars. Russian Soyuz Earth reentry capsules - the most widely used of all human flight vehicles - use an ablative glass-phenolic composite heat shield. It seems likely Russian Mars landing missions used the the same or similar materials.
The advantage of ablative heat shield is that it is cheap. The disadvantage is that it can be used only once.Non-ablative heat shields are desirable for spacecraft that are to be used more than once.The ceramic tiles on the Space Shuttle and Starship are examples.Carbon-carbon composites have been used on parts of the Space Shuttle that experienced less heating. Other refractory materials including metals are possible in principle, although they would not protect the cargo from heating and would likely require some spacing or insulating layer.
Non-ablative landing vehicles use entry descent and landing (EDL) techniques. A classic example was NASA's lunar landers, where the absence of an atmosphere on the Moon meant atmospheric breaking was impossible. For moon landings a spacecraft first used rocket propulsion to enter orbit. Subsequently a lander used propulsion to land on the Moon.
It's quite likely that (some) future Mars missions will use a similar approach, given the risk of direct atmospheric entry at high speed and the substantial deceleration involved, which would likely injure astronauts. A spacecraft will first use rockets to "brake" into Mars orbit and then a lander or the entire spacecraft will use EDL techniques to land on Mars. In these situations no heat shield is required, let alone an ablative one. In particular Robert Zubrin's Mars Direct mission proposals use this approach for EDL.
https://en.wikipedia.org/wiki/Mars_Direct
In contrast, SpaceX appears to be designing a direct entry and landing mission involving aerobraking as well as retropropulsion. Such an approach would see a variant of Starship, likely with non-ablative reusable shields, land on Mars. The same vehicle will be required to return the astronauts to Earth, hence the heat shields must be reusable.
