What 'private' usually means, and what it can mean
Most privacy pages in this category are describing careful handling of data they hold: encryption in transit, encryption at rest, a retention policy, a promise not to train on your recordings. All of that is worth having, and all of it is a promise about what somebody does with a copy of your meeting that they have.
The stronger version is not holding it. If the speech model runs in your browser, there is no copy on anybody's server to handle carefully, and the guarantee stops depending on the vendor's conduct.
The test for which one you are reading is simple. Open the network tab during a recording and see whether any audio leaves.
Why almost nobody does it
Running Whisper in a browser tab was genuinely impractical until WebGPU and quantised ONNX builds arrived. Before that, a browser could not touch the GPU and the models were too large to ship.
There is also a business reason. Server-side processing is where per-seat, per-minute pricing comes from. A product whose costs scale with your usage has to meter you; a product that runs on your hardware has nothing to meter, which is a worse business model right up until it becomes the reason people choose you.
What it costs you in practice
The first run downloads the model, once, and after that it is cached and works offline. A machine with WebGPU transcribes roughly in real time or better; one without falls back to the CPU and takes longer.
The honest trade is that a hosted service with a datacentre GPU will sometimes finish faster on a long recording. What you get in exchange is no minute cap, no upload, and a record that keeps working if the company stops existing.
Diarization is the harder half
Speech recognition on-device is now well understood. Working out who was speaking is a second pipeline: a segmentation model to find where the voice changes, an embedding model to turn each stretch of speech into a vector, and clustering to decide which vectors are the same person.
Both models are open and both run in a browser. The clustering is ordinary arithmetic, which means it can be unit-tested properly rather than being an opaque service.
The part that makes it useful rather than impressive is persistence: keeping a voice print so the same person is recognised next week. That print is biometric, so where it is stored is a real decision and not a detail.
Questions worth asking a vendor
Does the audio leave the device, yes or no, with no clause after it. Where are voice prints stored, and are they synced. Can I self-host, and is the schema published. What happens to my recordings if I cancel. Is the source auditable.
Every one of those has a one-word answer, and a vendor that needs a paragraph is telling you something.