Different brands of core drilling machines have different thread / attachments for attaching the core drill barrel. Most commonly here in Australia, most core drilling machines have a 1 1/4″UNC thread and are suited to most of the core drill barrels on the market.
Some brands like Hilti, have different threads, attachments for attaching a core barrel. Different models have different attachments, however they do offer a large range of core barrels to suit their drills.
Core drill thread adaptors are available to accommodate most type of core drilling machines. Most adaptors available will convert the machine thread / attachment to the 1 1/4″UNC thread so you have a larger range of core drill bit availability.
This is also the case for Dry core drilling as they are usually a 1/2″BSP thread. So therefore you can get an adapter from the 1 1/4″UNC to the 1/2″BSP thread.
Another great option available is to be able to run a core drill bit on a standard drill and / or hammer drill. Adaptors are available in a hex shank for a standard drill chuck, sds plus and sds max for rotary hammer drills. These are available for both 1 1/4″ and 1/2″ threads.
Below is a picture of many different core drill thread adaptors available on the market.