Madd Muttasil (obligatory)
Madd Muttasil (المَدّ المُتَّصِل): a Hamzah follows the Madd letter in the same word. It is obligatory; for Hafs by way of ash-Shatibiyyah its length is four or five counts. When stopping on a final Hamzah, four, five or six are allowed.
Madd Munfasil (permitted)
Madd Munfasil (المَدّ المُنْفَصِل): the Madd letter ends one word and the Hamzah begins the next. For Hafs by way of ash-Shatibiyyah it is four or five counts; by way of Tayyibat an-Nashr (طَيِّبَة النَّشْر) it may also be shortened to two (for information only; this book follows ash-Shatibiyyah). The reciter must be consistent: the length he chooses is kept for every Munfasil in the same recitation, and it is never longer than the Muttasil.
Madd al-Badal
Madd al-Badal (مَدّ البَدَل): the Hamzah comes before the Madd letter; usually it is a Hamzah that was changed into a Madd letter. For Hafs it is two counts only.