‘I’m going to a party on Saturday.’ means that you have plans now to go to a specific party later. ‘I will go to a party’ would never be said to have that meaning. But you can create situations where saying those words is correct English: Q. What are you doing Saturday? A1.I don’t know. Maybe I’ll go to a party. A2. I’ll go to a party but I’m not sure which one. In these cases you are making a conjecture about the future, and indicating that you DON’T have specific plans.

You're right, Lucy.

No, it's not saying your way is incorrect. It's just telling you which phrases qualify as "present continuous" tense.

No, you haven't been saying it wrong; it's perfectly good English. However, it's more usual to say 'I am going to . .' for future events about which you are reasonably confident. 'I'm going to see my parents next weekend'. 'I'm going to university next year'. 'I'm going on holiday to Japan in the summer'. If you don't yet have a clear plan you might say : 'I will go to see my parents next weekend if I finish my work'. 'I will go to university next year if I pass my exams'. 'I will go on holiday to Japan in the summer if I've got the money'. This form works better if there is some uncertainty about the event. You can use the 'I'm going to . . ' form here too, and it's also good. You can even combine the forms : 'I will be going to see my parents next weekend'. 'I will be going to university next year'. 'I will be going on holiday to Japan'. 'I will be going to a party on Saturday'. My advice is to become familiar with all these different forms, and not to worry about which is more correct: they're all acceptable and natural.

I think to some extent it's less an absolute question of correctness and more an issue of trying to say things naturally, as a native speaker would. For example, everyone will understand what you mean if you say, "I will go to a party Saturday," but under normal circumstances a native speaker would say, "I'm going to a party Saturday." Also, it's confusing, as under some circumstances, "I will go to a party Saturday" would be the natural choice.