Fulltext index doesn't work that way
it would find Zebra as long as there is a space or an interpunct before and behind it, so that ozt can idenitfy it a a word.
That's the function of the full text search and you can't change it.
A word like zebrajsduerhn would not be found by your query
You would change it to
SELECT * FROM SynonymWords WHERE CONTAINS( [words], '"zebra*"')
It taes some time to get used to it
Iyou want to have an exact search for word i would recoment to read this thread SQL Server query to match the exact word which handles this and also have an answer for regular expressions.
If you need something faster you should take a look at elasticsearch and opensearch, but these needs also some time to undertsand the concepts