I'm a little bit confused about the different loot drop sprites, as far as I can tell, I can only pick up the yellow ones, not the white ones, at first I assumed that that meant the yellow drops were because I killed the enemy that dropped it and white was because someone else did, but I've noticed that sometimes I'll be the only player who fired on a ship and it will spawn a white drop, or someone else will kill an enemy that I didn't shoot and it will spawn a yellow drop. What's the deal with those anyway? And what do the drops that are different shapes from normal mean?
You are correct in your assumption. The white ones are for other players. The only reason I can think of that they would even show up, is if you were in a team. If you are in a team the default method of looting items is "round robin" so you get one, then the next player gets a turn, then the next etc etc. until everyone has picked up one item.
Unless you're in a party, the only time loot that doesn't belong to you shows up is in a Deep Space Encounter or Fleet Action. So a player will be able to see white loot drops from many different mobs/players.
If you're in an open (pickup) team, then the looting defaults to Round Robin - each time there's a drop, it assigns it to a different person. IE, if you, me, and Bob are on a team, you'll get one, then me, then Bob, then you again. If you're not in a team, but other players are around, it's *supposed* to go to the team that did the most damage - someone flying solo in a Fleet Action or Deep Space encounter will rarely get a drop unless they actually killed the target without assistance. (That's my understanding of how it's *supposed* to work, in any case.)
As for the different shapes and colors - yellow glowing drops are ones you can claim. White ones belong to someone else. The ones shaped something like a mechanical pear are ship drops. Round spheres are usually ground drops (personal weapons and armor, or ground consumables.) Very rarely I'll see batteries or other random items with an odd rectangular marker, but this isn't consistent and I assume it's a bug. Generally speaking, you should never see sphere drops on space, or ship beacons on the ground unless something has glitched.
Yeah I also have a problem with this as I was in deep space and killed several targets solo and they all dropped white loot. I was not in a group at the time. Takes away the fun if you get no reward for doing all the work.