Events are actually side missions. They have more variance than encounters, but both serve as short detours, with an experience reward. Aside from that, they are quite different:
Encounters are marked out as triangles, on the map. Blue triangles for security-based encounters, green triangles for medical-based encounters, and yellow triangles for tech-based encounters. They are a lot more generic than side missions, and repeat themselves far more frequently, but they will reward you with supplies in the corresponding field.
Once you have completely unlocked access to your base of operations, you can spend these supplies to upgrade the security, medical and tech wings. In turn, these upgrades will give you a variety of benefits, including access to new abilities and perks. You will earn a lot more supplies from completing main missions, but you will have to complete roughly two thirds of each set of encounters, if you wish to earn enough supplies to completely upgrade your base of operations.
You can mark an areas encounters on the map by interacting with the notice board in the areas respective safe house.
Side Missions are marked out as pentagons, on the map. They offer more variety, and a greater challenge, but also offer more experience.
Each side mission will also reward a blueprint, used to craft gear at your base of operations.
You can mark an areas side missions on the map by interacting with the JTF officer at the respective safe house. Once you have completed all of an areas side missions, you will be given a mission to return to the JTF officer for one last reward. Upon speaking to the JTF officer, you will be given another mission, which simply directs you to the next safe house.
Completing a Region
As a side note, once you have opened the tech wing for your base of operations, you can purchase the Canine Unit for 200 tech supplies. The Canine Unit unlocks the Intel Discovery perk.
With Intel Discovery, completing all side missions and encounters in an area tags all undiscovered intel, within the same area, on the map.