What is the difference between an H-Bridge Motor Driver and Dual motor driver board?
Item 1 - The L293 has two H bridges and is a chip. 

Item 2 - The Ada fruit product is a circuit board with two chips and each chip has a single H bridge. 

Item 1 and item 2 are functionally very similar however Item 2 has H bridges that are superior.

Item 1 is a chip that needs soldering to a PCB and item 2 is a PCB with broadly the same functionality as Item 1.