Mixed cost is probably a cost like like electricity where there might be a fixed monthly charge and on top of that a charge related to each unit of usage.
A minimum charge is quite similar. However, the fixed element will include a charge for minimum usage (eg 5000KWH). Up to that usage there is no additional charge but above that there will be a charge per unit used.
So, it’s like mixed costs but the variable element does not start until a certain amount of usage (the minimum charge amount) has been incurred.