And what are the other diminutives?
You're taking it from wrong side. All these endings are to make diminutive without any difference in meaning but in degree.
Polish diminutives (zdrobnienia) have different roles in itself - the same as in English - but in English you have so small choice of wordings here.
It can mean smallness, lightness, tenderness and of course by contrariness - so popular both in English and Polish - toughness, and extreme hugeness.
And the endings. The whole mess about it is due to medieval history of Polish language. There were 2 small semivowels which was lost. They are called yers - soft one and hard one.
They are responsible for all these confusions with declination of piesek (doggy): pieska, pieskowi, pieska, pieskiem, piesku.
All the rest is a plentifulness of tenderness:
0) pies, kamień, Jan | kura, gazeta, Anna
1) -k: piesek, kamyk, Janek | -ka: kurka, gazetka, Anka
2) -cz-k: pieseczek, kamyczek, Janeczek | -cz-ka: kureczka, gazeteczka, Aneczka
and so on...
And all these not only with nouns but also with adjectives and adverbs:
mały (small): maleńki, maluśki, malusieńki
drobno (finely): drobniutko, drobniuteńko, drobniusieńko
After some training with word formation rules you can easily create a diminutive of your choice with every word and every degree of tenderness, but beware - some of them will sound idiotically and not used at all - but quite well intelligible by your listener.