In Drupal 6 there are the following database tables:
What are the equivalent tables for Drupal 8?
All tables by the taxonomy module are prefixed with taxonomy_ since Drupal 7.
term_data is now taxonomy_term_data but also taxonomy_term_field_data, as it is a translatable entity. Never interact with those tables directly, use the entity API.
term_node is taxonomy_index, but it is only a secondary index you can read from there, but the primary storage are the entity_reference fields that point from nodes or any other entity type to taxonomy_term. So if you want to change values, you need use the entity API as well.
Taxonomy works very different than in Drupal 6, where you had to enable a vocabulary per-node type. Now terms work exactly the same as any other refeence, between nodes and other nodes, nodes and users and so on. The only left-over of the old system is that an index table is maintained specifically for node -> taxonomy references.