So, this is possibly a dumb question, but is there an unofficial title for the third or fourth son of a king? Like the first son is "the heir" and the second is "the spare" but is there something similar of the third or fourth son? Or is it just third in line and fourth in line? I've tried looking it up online but I can't seem to find anything about it.
Basically, Mark C. Wallace's comment is probably the correct answer but, as there seems to be some interest in this question...
The only unofficial names for 3rd and 4th sons in use appear to be spare and (less commonly) spare to the spare. There are many online sources (both 'history' and 'non-history') using spare for third, fourth, fifth etc sons, and in the UK these now include daughters.
Unexpected Heirs in Early Modern Europe: Potential Kings and Queens (Valerie Schutte, ed.) uses spare for King Henry III of France, who was the fourth son of Henry II of France, and also for Gaston, Duke of Orléans, third son (though 2nd surviving) of Henry IV of France.
The Historyextra site mentions ...plus at least one spare in case of accidents while spare to the spare is used with reference to Prince Edward, 4th son of Elizabeth II in this (not very historical) book.
I think it mostly depends on the monarchy you are dealing with ; It seems to me that most of the "direct" line of succession during the Old Regime in France were all "Princes".
During the two French Empire, the only one to have a "special" title was the direct heir, titled "Imperial Prince", while others are only titled "Prince". Visit this Wiki here if you can speak french or can translate it easily.
If you are interested in heraldry, Cadency Marks differentiate the shields of each children, with special symbols for the 1st, 2nd, 3rd, etc. But this is very dependent on the country and time period.
And in iberian monarchies, Infante was the title given for all children of the king who were not the first to inherit. e.g., "Prince Henry the Navigator" in Portuguese sources is known as "Infante Dom Henrique, o Navegador".
Moreover, to complement ShadowEntun answer, the eldest daughter of the english monarch is a Princess Royal
But, except for the cadency marks, I have never seen specific and fixed titles for each and every royal child.