Again, I have no personal experience of these, but I know a range of electrical and mechanical systems were used for the engine order telegraph, depending on the era.
https://en.wikipedia.org/wiki/Engine_order_telegraph
On modern ships everything is controlled electronically from the bridge of course, apart from when the emergency backup arrangements are in use.
The Royal Navy in particular distrusted electrical communications and believed they were vulnerable in combat. Most RN ships were still using speaking tubes and engine telegraphs well into the 50s.