just some additions.
the short name is not necessarely shorter, it can be kinda like John vs Johnny, which is not shorter at all. Some russian names have an established short form, or even two, while other have none. This has nothing to do with the length of the actual name (my guess it is more related do the historical usage of the name). For example, Anna has a short form, Anya. But Alina's short form is less known (my guess is that this is a fairly "new" name in Russia, so there is no established short form).
One short form can be used for several names, for example, Alya is a short for both Alexandra and Alina, and Stasya for both Anastasia and Stanislava.
Usually there is a predominat short form, for example, Alexandra is pretty much always Sasha, and only rarely Alya.
those short names are established things, its not something made up for a specific person (the person can chose what short form to be used when several are available).
short names can be used while talking to friends and kids, and it is overall fine (no major offence) to use it while talking about a young person you dont know (for example, a skater).
Diminutives are friends and family only. There is a whole gamma of diminutive forms for names.
For example, for Evgenya, you have the short form Zhenya, and then can have diminutives such as Zhenechka or Zhenka (and a few other, more exotic suffixes). Those suffixes have somewhat different meanings (so i do not recommend using those unless you are russian, because dude, this is complicated), so for example Zhenechka and Zhenka would be used in different situations.
Just repeating, the diminutives such as Zhenechka, Mashka, Alinka are usually reserved for friends and family, and there are also many nuances about the usage of those names. Using such diminutive improperly can be even disrespectful.
For example (just to not bring skaters into it), my name is Tatyana.
The short form of it is Tanya. All my relatives except for my mom call me that.
My mom calls me Tanechka and Tanyusha. That is sweet, but i am a bit antisocial and not girly and not cute and feel somewhat uncomfortable when people call me that, this form does not fit my personality.
My friends call me Tan'ka. This is for friends only. This is also used by relatives when they are gossiping about me (though they dont say it at my face, never). And if a random person that i dont know well would call me that, I would be mad because that would be disrespectful.
