What determines the class of private ip addresses?
Nothing because network classes are dead (please let them rest in peace), killed in 1993 (over 25 years ago, before the Internet went commercial!) by RFCs 1517, 1518, and 1519, which defined CIDR (Classless Inter-Domain Routing). Modern networking does not use network classes.
If you want a history lesson, this answer explains what used to define network classes.
Your question is now completely different after you got answers for the original question. That means you should have asked in a different question. This is very bad for for SE sites.
In any case, you are free to configure any Private IPv4 addressing from any of the Private IPv4 address ranges on your own private network. There is no standard requiring any particular range on any network.
What determines the private ip addresses?
RFC 1918, Address Allocation for Private Internets defines Private IP addressing.
So, who determines what kind of ip I am going to get. Who decides
whether the ip would be 10.x.x.x or 192.x.x.x.
What you have at work was configured by the network administrators, likely assigned by what is configured on a DHCP server, although it may be statically configured. What you have at home is based on how you have your equipment configured (probably just took the equipment default), most likely assign by a DHCP server in a consumer-grade router (home networking and consumer-grade equipment are explicitly off-topic here).
And why are there different types of private ip.
Back when private addressing was created (prior to CIDR), classful addressing was still common. The reasons for the three address ranges are explained in RFC 1918:
If a suitable subnetting scheme can be designed and is supported by
the equipment concerned, it is advisable to use the 24-bit block
(class A network) of private address space and make an addressing plan
with a good growth path. If subnetting is a problem, the 16-bit block
(class C networks), or the 20-bit block (class B networks) of private
address space can be used.