Temporary
Temporary custody is when the legal proceeding is ongoing and until the decision for custody is made, a judge can grant temporary custody for one of the parties to look after the child in the interim period.
Sole
Sole custody is when one parent will have the exclusive authority when it comes to the parenting decisions and wellbeing of the child.  Even if sole custody is granted your former partner may still need to be consulted before making any final decisions about the child's parenting.
Joint
Joint custody can be done either through an agreement from both parties, or through the court. When given joint custody it means that both parties have equal responsibility even though they may live apart. Both parties are involved in making final important decisions in the child's life and upbringing.
Shared
Shared custody is a specific subtype of joint custody and usually involves the child spending equal time with each parent.