What does "at scale" mean?

Whats does the expression at scale mean?

Does it mean "on a larger scale" or does it mean "at a level appropriate to the what's available"? I came up with these two definitions by looking the expression up on the internet, but I still feel very confused.

Here are two sentences:

Over the course of that first afternoon, the next months, and finally over several years, we honed our practice activities into tools that could help make teachers better, at scale

If you seek to do somethings great, you most likely live a battle for talent – for smart and capable people who can do great things at scale.

See scalability (Wiki)

scalability is the ability of a system, network, or process to handle a growing amount of work in a capable manner or its ability to be enlarged to accommodate that growth.

In the given cases,

tools that could help make teachers better, at scale

implies those that could measure up to the size of the task.

people who can do great things at scale.

similarly implies people who can do great things when those things manifest in a real-life (larger) systems. It is easier to demonstrate a prototype supersonic aircraft, but extremely complex to build a really usable/ commercial product of the same design concept.

We do not say on a large scale in this context, but instead we say at scale, because the magnitude could either increase or decrease from time to time. Adapting accordingly and producing comparable results in all cases is a challenge in itself. Think prosthetic & orthotic devices, for one.

In the software world, the idea of "at scale" refers to automation or other tools that lets you execute some needed task or great idea easily, no matter how many machines or applications or whatever need to be changed. In other words, if you have to go and change each machine or application one by one, then clearly you can't operate "at a large scale" effectively. If you have some way to just press a button and have all the changes made automatically, no matter how many machines or applications you are talking about, then you are able to make those changes "at scale."

In the example the questioner gave, my guess would be that they were creating training tools that can be delivered locally, and do not require the experts who created them to go deliver the training. The former could reach an infinite number of teachers, i.e., "at scale"; the latter could not.

I think it's the same as 'at a large scale' when used loosely. I've got an example that reads 'Provide powerful and easy-to-use solutions at scale.' This, in my opinion, means that those solutions are intended for a large group of recipients, not just a few, which is why I think the meaning is the same as in 'at a large scale.'