TAFE and College is, generally speaking, a public and private vocational educational institution respectively. Every private educational institution authorized by the Department of Education can grant a degree equivalent to that of a public educational institution. The credits gained from private colleges can be recognized when entering universities. However, if earned a very small private college, credit recognition can be limited by universities. Therefore, you need to choose TAFE/College carefully depending on the purpose of your enrolment: learning skills or entering a university.   
So-called Community College, in U.S.A, can be considered as an Australian private college and a number of them, specially those supported by a large education fund, are linked to universities in a form of ‘pathway’.

TAFE

Hundreds of TAFEs are there throughout Australia. Partly because the schools are funded by the government and partly because permanent residents and citizens are eligible to be subsidized their tuition fees by the government when enrolling TAFEs. Names of TAFEs are different in each state; New South Wales and Tasmania have set a common name as NSW TAFE and Tasmania TAFE. They put a campus name in addition to indicate the area of study each campus is offering.
Studying period varies with the type of a degree; Certificate I, II, III, IV, Diploma, Advanced Diploma, Association Degree and Bachelor.

Bachelor is normally granted by a university, however, standardized courses such as a business degree can be offered by a TAFE.

College

International students MUST study full-time (more than 20hours/week) while most of local students choose 'Apprenticeship’ mode where they can combine 10hours/week of work and 10hours/week of studying. Total studying period for a degree is longer for local students e.g. they could study for Certificate III over appx. 3 years.

A college in Australia may refer to a private institution of tertiary education; it ranges from small, local, private institutions to those operating as a part of a university. Colleges may offer more specialized courses that are not easy to be found in TAFEs, providing better facilities and equipments; students need to make a careful choice based on what they wish to study.

Until recently, many students have chosen private colleges that offer quality programs at affordable fees, for the purpose of applying for a Permanent Residence. However, the significant changes in the immigration policy announced in 2010 urge that students should make a careful decision when planning to study in Australia.

Large private college

Some private colleges are run by a large education fund; they may be closely related to a specific university or share their facilities with a university. Students in such private colleges have a head start in going on to the related university and their credits are readily recognized by the university thanks to the linked curriculum

e.g. Martin College, IBT Group, Kaplan, etc.