It's conceptually similar, but is probably more properly related to Mantle (the AMD API later donated to Khronos, which they developed into Vulkan) and its initial release predates that of Vulkan by ~18 months (Metal was announced in September 2014 for iOS, the OSX port was released in June 2015, the initial release of Vulkan was in February 2016).
Somewhat, but with more (forced) automatic resource management.