Different templates for different category tags

Is there any method to create different template in a theme for different category tags search?
For example, I have category ‘blog’ and category ‘glossary’ – there is no any similar tag for both categories.
I need to open tags from blogs this way:
/blog/tag/any-tag-blog
/glossary/tag/any-tag-glossary

what method can I use in the theme for splitting tags result and to have different template pages for these categories?