Actually a modern "sand battery" does have to be sand or at least a granular material. The difference between a sand battery and thermal mass is that you use a conveyor to superheat small fractions of the sand, allowing the isolation of high grade heat.

If you have a single kWh to store and 1 ton of sand to work with, you could heat 1kg of sand to hundreds of degrees (sand battery), or 1 ton of sand by one degree (thermal mass).

1 ton of slightly warm sand is useless, while you can extract the high grade heat from the 1kg and get your 1 kWh back.