What is the difference between load balance and application delivery controller?

Loadbalancing is one of the feature of Application Delivery Controller 

Simply put, ADC is advanced load balancing, it includes other techniques to improve application performance over the LAN/WAN like compression, caching, filtering and even some added security features like prevention of DDOS attack, etc..

ADC can accelerate the performance of applications delivered over the wide area network wan by implementing optimization techniques such as compression and reverse cashing. With reverse caching, new user requests for static or dynamic Web objects can often be delivered from a cash in the ADC rather than having to be regenerated by the servers.