Maintenance is support for a spouse. They can use that for daily living expenses, but it is taxed to the spouse who's receiving it and it's a tax deduction for the spouse who is paying it – that is one of the biggest differences.
Child support, on the other hand, are funds paid to the parent who has the children the majority of the parenting time. Child support is not taxable to the parent who's receiving it and the child support is calculated based on net income, whereas for maintenance the calculation is based on gross income because taxes come into play. The payor spouse again takes the tax deduction and the payee spouse is taxed on the maintenance. For child support it will generally terminate when the child turns 18 or graduates from high school, and with maintenance it will most likely be based upon the guideline – which is the number of years you've been married, and it may or may not be linked to the age of the children.