If your categories would benefit from being custom post types, i.e. you want to store data for each category, then this is where CPT-onomies come to call. You'll have to give each set of categories a unique name, like "series_categories" and "group_categories", and create post types for them in the CPT-onomies admin area. Then, in the "Register this Custom Post Type as a CPT-onomy" section, you can attach each category to its corresponding custom post type to create your CPT-onomy.
If your categories don't need to be custom post types, i.e. you just need the term and that's all the info you need for each category, then you just need plain ole taxonomies. You still need to give each category a unique name so you can separate them out, register the taxonomies and attach it to its corresponding custom post type.
The code is pretty simple to register a taxonomy, but there are also a few plugins that will help you out if needed.
Check out the codex for more information on taxonomies.
I hope this helps!