In my previous role as a builder, I have witnessed what all three bring to the table. Which one to use, depends on the individual client, project, and budget. Here is my take on a very basic view of each:
To be recognised as a building designer in Victoria, Tasmania and Queensland, a building designer must be registered. Other states are in the process of formal registration to improve the quality of building design. Quite often, a draftsperson will look to advance their knowledge and skill and seek further education to become a building designer.
A building designer usually completes a 2-year Diploma in Building Design. The focus is a little less time/expense on the artistic process (see architect) and more on the practical use of space and energy-efficient design which are still visually appealing. If you are after a design of common sense, and the right ideas to reduce builder costs and maintenance, choose a building designer or a good draftsperson.
There is no formal qualification required to be recognised as a draftsperson. Some study drafting at TAFE, and some learn their skills on the job. A draftsperson will offer advice based on your input and produce plans of varying quality depending on their experience.
For the record, although I am a building designer, my rates are comparable with standard draftsperson rates. The most important aspect of your decision is to choose someone who shows a genuine interest in your needs and is not afraid to suggest options to achieve the best outcome for you and your budget. Builders are on the front line, so they see who is good at their job, and who is not, so ask them for recommendations.