It was called partitioning and existed long before. The syndrome of "new" people believing they have invented something, naming it without realizing it already had been invented long ago and already had a name, is quite common.
I'd always assumed they were the same thing, and the choice just gave you a hint of the speakers background. Old school DBAs are way more likely o say "partitioning", game devs or young FE devs will almost always use "sharding".
With this, sharding and horizontal partitioning are essentially the same, and the term partitioning by itself just means splitting up the data in some way (could be horizontal, vertical, or other).
That said, I've also heard people use shard and partition interchangeably in the general form, in which case, you get "horizontal sharding" and "vertical sharding".
I'd start by googling horizontal vs vertical partitioning.
That's not correct: https://en.wikipedia.org/wiki/Shard_(database_architecture)#... al_partitioning
For example, horizontal partitioning is often used within the same schema on the same instance in order to have separate indexes for (say) current vs. historical data. That's not what is meant by sharding, however; shards are separate instances.
> Sharding goes beyond this. It partitions the problematic table(s) in the same way, but it does this across potentially multiple instances of the schema.
"Beyond this" but still "potentially across multiple instances". Anyway, with your framing sharding kind of becomes "distributed horizontal partitioning".