There is no specific number of hours that makes one worker part-time and another full-time. A part-time worker legally just means any worker who works less the normal full-time hours in that workplace. The rules apply to 'workers' which covers some consultants and contractors as well as employees.
Part-time workers have specific legal protections prohibiting less favourable treatment as compared to full-time workers. This impacts particularly on pay and benefits.
Part-time workers are also entitled to a written statement of reasons for any treatment that is less favourable than that of full-time workers.
Part-time workers are statistically more likely to be female than male. So, treating part-time workers less favourably may also be indirect sex discrimination. For more information, read Equal opportunities.