Two process which could result in different gametes occuring are random segrigation and crossing over
Random segrigation: When creating only one zygote, only two gametes are required to do so, however, there are more than one different groups of chromosomes that make up different gametes.
This means that the chromosomes the gamete gets durring meiosis are completely random, giving thousands of different comibinations of chromosomes.
This gives different gametes.
Crossing over: This is very common in meiosis. When the Chromosomes are in their homologus pairs, the genetic code from one of the pairs of "arms" become wound up like rope and finally break off, switching the code in the DNA. This will only happen with whole parts of the genes, so all the genes are there, just in different coding.