Synergy
The term comes from M&A and refers to scenarios where the whole (after a merger or acquisition) is worth more than the sum of the parts. For example, a steel foundry which acquires a competitor and can now buy iron at a lower price because it buys in higher volume. The increase in profitability of both foundries from the decreased cost of iron is a "synergy".
Value-add
Comes from Michael Porter (I think) and refers to the idea that each of the activities a company performs on their inputs before the final output should add value to the final product. If the company is unable to add value through one of those activities it's something they should pass to another party. This leads to phrases like "is our customer service call centre a value-add or should we outsource it?"