Deliberate practice is the highest form of practice according to Anders Ericsson and Robert Pool (the authors of the book Peak). Based on the scientific study of expertise, they classify several forms of practice. From less to more effective:

Naive practice. You practice music by playing it. You practice medicine by doing it. You practice driving by doing it. Ericsson and Pool cite studies showing that this is not very effective at increasing, or even maintaining, skill. Doctors are (on average) at their best shortly after getting out of medical school, and gradually decline in skill thereafter despite their continuing "practice" of medicine. Similar observations apply to other skills.
Purposeful practice. This is practice which (1) has well-defined goals (such as doing something 3 times in a row with no mistakes), (2) is focused (the person is intently interested in improving, rather than having their attention elsewhere), (3) involves feedback, (4) involves getting out of one's comfort zone, practicing things on the edge of one's ability.
Deliberate practice. On top of the requirements for purposeful practice, deliberate practice is informed by an understanding of how to do well. In the best case, this understanding is conferred by a professional teacher (a "coach"). This teacher will be able to evaluate where a student sits with respect to the various necessary sub-skills, recommend specific practice tasks to improve sub-skills which are lacking, and give advice about how to improve technique.

The authors note that purposeful practice can result in getting stuck if you learn bad form (they don't use that term, but what they describe is very close to the concept of "good form" from the CFAR handbook (page 19)). Bad form means that practice is ultimately instilling bad habits, even if it creates local improvement. Good form means that practice is taking you down the path to mastery in an efficient manner.

Due to the necessity of having an experienced teacher, deliberate practice requires a highly developed field. However, it is also common to use the term "deliberate practice" for anything which is distinguished from purposeful practice by the presence of a theory of skill and practice guided by that theory, whether or not that theory is tried-and-true, and whether or not an experienced teacher is involved.