Why does the
markov-chain tag get changed automatically to
markov-process? I had an answer addressing the difference between these two things here.
It's called a "synonym." They are listed at https://stats.stackexchange.com/tags/synonyms.
When it's discovered that two tags mean the same thing, one (usually the less popular and less descriptive) is mapped to the other. The mapping can cause the synonym to be replaced by its alias. All synonyms are supposed to perform as alternative names for the same functional tag, which means it shouldn't have an effect on counting answers for tag badges, etc.
People with sufficiently high reputation (either overall or in one of the tags) may propose synonyms and vote to approve them. Many of these meta pages are also devoted to public discussion of possible synonyms.