Assuming a 88-column, 6mil-row table, “Horizontal” means horizontally pushing a knife across all 88 columns, splitting 6 million rows into 3 millions each.
Sharding can work on noSQL too.
GS PWM positions table had 9 horizontal partitions for 9 regions.
“Partitioning” is a more generic term and can mean 1) horizontal (sharding) or 2) vertical cutting like normalization.