Nina I am wondering if it is a misprint and the comparison is between
1) the toy of the girl - an alternative way to say this would be "the girl's toy", it is the genitive case, phrase to use when referring to a toy belonging to the girl, a specific girl.
2) the toy of a girl - again this could be "the girl's toy". The difference with the previous phrase with the change of "the" to "a" is that use of "a" here means it is not a specific girl as when we use "the" girl
3) a toy of a girl - here as in the previous (number 2) the girl is not a specific girl and by using "a" we are also removing identification of a specific toy, it could alternatively be stated as a girl's toy
4) a toy of the girl - the phrase is identifying a specific girl but not a specific toy, alternatively stated as the girl's toy.
Hope this is of some help for you.