Hero Missions: Story missions. Game gives you the character you will play. A Day and Once An Avenger(Latest Thor Mission) are the hero missions we know.
War Zone Missions: War Zone's aren't a mission type. Everything that is not a hero mission, is a war zone mission. There are a lot of War Zone mission types. Everything i will talk about after this is a War Zone mission.
Iconic Missions: These are multiple missions, combined to forge a story. You can't choose a character. Once you finish an iconic mission chain, you will get the Iconic outfit of that character you played as. So, probably each hero will have 1 iconic mission chain. We don't know if they have co op, but i don't think they will.
Faction Missions: Faction leaders will give these missions. We will get intel and supplies for factions. And we will have to defend them from AIM. Our Helicarrier will grow as we do these missions. We will get these missions from the Helicarrier and the Resistance base.
Drop Zone Missions: Very basic missions. They have 1 objective. Defend Allies. Sabotage an AIM Structure.
Vaults: These will be like Raids. They will be hard to find. They will be large. We will be able to explore them. First, we will have to find the location of the Vault from hidden Shield caches. Big battles awaits us Inside.
Hives: Outposts. Enemies will come in waves. Each wave will be harder.
Villain Sectors: Strikes/Dungeons. These will end with a big boss battle. They will have notable Marvel villains.
Thanks for reading. We will see Drop Zone Missions in the July War Table stream. They said Beta will have a lot of things. Definately wait 1, maybe 2 Hero Missions. They will show drop zone missions, so wait 1 of them. And i think Villain Sector could be included.
Destiny 2 Beta had the first mission, a strike and pvp. So villain sector makes sense. They can't have faction missions or iconic missions. They can have spoilers about the main story. They won't have a raid in the beta. Maybe we can also get a Hive, but don't wait for that too much.
Hero Missions and drop Zones are guaranteed with maybe a villain sector.