Most people will call any of those types of tools a crow bar, but when you work in factories or on building sites you have to learn the specific names so that you can ask for the specific tool you're looking for.That's interesting and a little confusing. I'll just call it brekkjern, that's what it's called here.
The Crow Bar is very specific and is named differently to all the others. It comes from ancient roman times, a device they invented for boarding other ships that they called a Corvus. (crow) It was a heavy boarding plank with a large metal spike in the end that they'd drop onto another ship when they were close enough. The metal spike would stab in to the other ship's deck preventing them from separating. The common people found that these metal spikes were great for digging with.
Corvus (boarding device) - Wikipedia