i am curious about if one cartridge can be used on all types or brands of
batteries?
Welcome to ECF, rw...
To answer your question... no, (without an "adapter") you must mate up the correct
thread type. There are a variety of connector thread variations that have been developed, and have been around for a good long time. The most common, universal, popular - call them what you will - are the 510 and eGo.
One of the reasons for this is that they are typically used in combination on the ubiquitous stick form factor or "eGo battery" type. Both are the ground or negative element of the electrical connection... with the 510 being the internal female thread - the eGo being a outer male thread... with both using the common positive.
Other thread types... like 808, 801, 401, 4081, 901 and 808D are slowly fading into the sunset. However... there are still plenty of
adapters out there, which allow a near universal mating of otherwise mismatched thread types.