What is the difference between part-time and full-time study in postgraduate courses?
I don't have any private job experience in Scotland or Netherlands and I don't know your conditions as well, so I don't really know what suit's your conditions indeed. I am focusing on your first question here.
Full-time learning is mostly suitable for the candidates who are not aiming to work outside the university. For instance, students who are able to stay full-time in the university and do their academic chores are more encouraged to apply for these discipline. Part-time learning is more suitable for those who want to work outside the university as well as attending their classes and conducting their research at the university. This type suits the people who work outside academia and are not willing to be at the university all the time.
Please note that, some universities hire or pay their research students while they are studying at the university. This does not mean that those students are part-time students because they are simply working or hired at the university. These are full-time students who are doing academic work. These are different that part-time student who works in industry.
As you mentioned in your question that you are interested in several courses, it comes to my mind that it does not make any difference to you to study in a specific area; so this eases your way to find a program for yourself. As an instance, in a university, one department may not offer part-time degrees to the applicants while the other department may offer various taught and research part-time programs that the prospective student can easily choose one for himself.
However, as far as you are seeking for a degree with the insight to your professional career, I encourage you to choose the course and degree which helps you with your professional responsibilities and your interests.
Don't run, Walk! Please choose a part-time program wisely;

Please carefully read the regulations of the programs you are applying to and check the minimum requirements for part-time degrees at the university where you want to study. These programs may require some extra application process, interviews or documents for their applicants.

The duration of the part-time degree is longer than a full-time degree. For instance, a masters part-time degree will have two year duration compared to one year full-time study. Please note that the duration of the degrees varies from one department to another and one country to another.
If you are going to do research in your part-time program, please note that some part-time degrees require their students to do full-time research during their studies. I mean, you have applied to a part-time degree. Although you are allowed to study for a longer period of time (for instance part-times may take classes in four semesters while full-times are allowed to finish their classes in two semesters) but the course requires you to spend two semesters full-time research as well. So, please check whether these conditions exist or whether you are eligible for such programs or not.

You may need some scholarships/funding to support your studies financially. Then you should double check whether the scholarship covers the part-time degrees or not. To my best of knowledge, some scholarships require the students to attend only full-time courses.

Check the cost of the program you are applying for. Although it seems that the full-time students will pay lower fees compared to the full-time students, but, keep in mind that the total payment of both disciplines may be the same and only the part-time student may pay lower amounts of money in each semester. On the other hand, there may be some part-time degrees which are due to higher educational fees. As far as the rules are different in different countries and departments, please check the financial part carefully before you apply for any degrees.

Check the accommodation and housing for part-time students as well. Although it seems that you are staying with your family; if you are seeking to stay in another city where you are working and in this city, you are seeking a part-time degree; please check whether they offer housing to the part-time students or not.

Part-time degrees may only allow you to work inside the city where the university is located. So, if you are working outside the city, check the regulations of the university and see if you can manage to attend your classes regularly or not.

Part-time learning differs from distance learning and online degrees. These disciplines have different regulations and their degrees may have lower or higher values in the industry you are working. As far as you need your degree for your professional career, make sure which type suits you well and do not think these degree-types are the same.

Pay Attention to your studies too. Please don't think that because you are working and you are a part-time student; you are allowed not to study and not to attend your classes and fail the exams. Your role at the university is studying and research, whether you are a part-time student or full-time student.
But, as a part-time student, you will have less credits each semester that you will be able to study besides to work. So, still pay sufficient attention to your courses.

Also, please check the visa type you are holding and whether you are basically allowed to work or not. Some international students are allowed to work a limited amount of time each month or each week. If you are thinking about working in another country and studying part-time there, please think about such things too.