In British English (as far as I am aware) Part-time usually refers to 'not the whole working week'. So you can study for a degree in 3 years full time, or 5 years part-time. Part-time does not give an idea of something being temporary or 'short'. In the situation you describe, it depends perhaps it is a short course, or a modular course, perhaps?

In the USA, a full-time college student is usually defined as someone taking at least 12 credits per semester. A semester is about 4 months long, either from August/September to December, or from January to April/May. Each college class is assigned a number of credits. For example, an "easier" class may be 1 or 2 credits. A harder class may be 3 or 4 credits. By this definition, a part-time college student in the US is someone who takes 11 credits or less per semester. There are probably different systems in different countries. Also, I'm not sure if you are referring to college students or grade school students. This is just how full-time and part-time are defined at a typical 4-year university in the USA.