I am sure others can elaborate more eloquently and extensively, but maybe i can clear up a small misconception, as Prussia isnt necessarily "Prussia".

The Prussia that became a major European power is actually the former margraviate and later prince electorship (Kurfürstentum) of Brandenburg. As with many European feudal familiy states, Brandenburg expanded its territory gradually and rather slowly at first, mostly through marriage and inheritance. The most notable developments towards the later great power you are talking about happened in the 17th and 18th centuries.

It is really important to understand that the Prussia you are talking about as Polish vassal was the remainder of the Teutonic Order state that was transformed into a secular duchy. This Prussia was indeed a Polish vassal - Brandenburg never was. After having acquired Prussia, the prince elector of Brandenburg within the Holy Roman Empire was also duke IN Prussia (the in becomes important later).

I could go in detail about the so called "great elector" (großer Kurfürst) and his hunger for recognition and .. glamour, but let's keep it short at: the prince elector and more importantly his son Friedrich (all Hohenzollern) wanted to become equals with the greats in the empire, meaning king, and spent vast sums to lobby for being raised to that title. As the emperor would not grant such honor to a potential rival within the empire, an expensive compromise was struck, namely that he could call himself king, but not within the empire. As the former teutonic order lands were located outside the borders of the empire, the prince electors of Brandenburg were allowed to call themselves kings IN prussia, not of. So for lack of a more simple explanation, basically they declassified their original title of Brandenburg and started calling themselves Kings in Prussia. Again, they were never a true vassal of the king of Poland but were using the title to elevate themselves to grander spheres. Poland was technically overlord of the "original" Prussia and would of course not be happy with this, but was in constant struggle with itself and militarily insignificant at that time (basically having the title of king of poland frequently auctioned off to foreign rulers).

I am sure you have heard of Frederick the "Great" and his father that was as vital for Frederick's greatness as Philipp of Macedon was for Alexander's success, as "the soldier king", was not fond of wars, but really obsessed with being ready for them (meaning he built one of the most formidable armies of the continent at the time). When he died, Frederick the hazardeur and "hot blooded conqueror", disregarded all diplomatic decorum of the time and invaded rich Silesia, nipping it from the Austrians, when the opportunity arose during the Habsburg inheritance crisis. In three wars this was made permanent and only through the robust state his ancestors created and his remarkable genius on the battlefield (and a lot of luck), Prussia rose to the smallest of the 5 great powers at the time. Neither Poland nor the Habsburgs were able to effectively resist, the HRE was dissolved less than 20 years after Frederick's death - Poland even ceased to exist during Fredrick's reign due to him and Catherine "the Great" slicing it up among them. Being a major benefactor of the congress of Vienna, Prussia was able to massively gain territory in the west of the former empire, cementing Prussian strength.

This is a drastically shortened version of what happened and there are many factors that play into almost every segment i touched on, so dont take this oversimplification verbatim, but to answer your question: Prussia is not necessarily Prussia.

Source (among this being a major part of one of my theses): Kunisch, Johannes: Friedrich der Große, ein König und seine Zeit; 2004.

Edit: grammar & sources

It didn’t, as such. The Prussian state as we know it was mainly the descendant of the Margravate of Brandenburg, which was already a major component of the Holy Roman Empire (HRE) and not a vassal of Poland. Prussia and Brandenburg came to be in personal union, and while Prussia per se was in a sense the less important of the two, the fact it was outside the HRE allowed the Hohenzollern dynasty to use the title ‘king’ (which for land within the HRE they were not). That’s why they preferred to use the title King in Prussia rather than Prince-Elector of Brandenburg: not because of the state, but the accompanying title of ‘king’. And fair to note that they chiefly resided in Berlin. Eventually, their entire state came first informally and then formally to be called Prussia.

Brandenburg was not always the most powerful of the of states within the HRE (for centuries Austria, Bavaria and Saxony being more significant), but it was still one of them: its margrave had been one of the seven Prince-Electors - on paper the most significant rulers within it, who got to elect the Emperor - since the 13th century, and it always ruled a large part of north-eastern Germany. And the acquisition of the original Prussia itself was hardly insubstantial, and only helped to consolidate the Hohenzollerns’ power.    

The 18th-century militarist rise of Prussia to great power status, challenging the Habsburgs under the first two Fredericks, Clausewitz, Bismarck, until it became the predecessor state of the German Empire and Germany today, is a massively complex story about which much is written, but I think this first point is the main issue of slight confusion behind your post.

(With some similarities, the state called ‘Sardinia’, ruled by the House of Savoy was really centred in Savoy and then Piedmont, not the island they later acquired, so it is not a question of how Sardinia itself, which was never as powerful, managed to take up so much territory - but for similar reasons they could take the title King of Sardinia.)

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