Basically Fulltext Native uses phpBB's own search algorithm by building word-post-pairings. On large forums this information, which is stored in the database, can affect search speed (if my database knowledge is correct). The upside of this method is its independence from the database type (MySQL, MSSQL, Oracle). However, if you have MySQL, you can use its built-in fulltext-search which should be faster. Almost all shared-hosting webhosters use MySQL.
As for the 3-letter-abbreviations: MySQL is configured to index words which are 4 letters or longer. Maybe your webhoster can help you with changing this setting. One-letter-words should be possible with MySQL's fulltext index but I doubt any webhoster will be willing to configure that for you. With phpBB's method it is possible to set the min. characters to "1" but it'll cost you space in the search tables.