How are they different? And are they different enough to warrant two tags?
The existing explanation for the training tag is
The practice of martial arts. How, what, where, when, why.
And the existing explanation for the practice tag is
Practice; training; using a martial art for the purpose of building strength, speed, muscle memory, refining or learning techniques. Use this tag when your question focuses on learning your martial art in a non-competitive environment, either supervised or unsupervised practice.
Is there an instance where only one is applicable and the other is not? I think that these two tags could be merged into one. It will create less confusion when a user is trying to select the right tag. Training is "the process of learning the skills you need to do a particular job or activity", and to learn something, one needs to practice. Basically, when one is training, they are practicing their craft.
If that is not something the community wants to do, then we should discuss (here) the factors that make them different, so we can add some explanation in the body of the tags and improve them.