Mission skills are linked to crafting, but not to the same skills that the gathering skills are. All mission skills have missions that reward companion gifts, and all have missions that reward something used by a crafting skill. To send a companion on a mission, select the mission skill from the crew management screen and select the mission you'd like the companion to go on.
Some missions give items that are more useful to a profession, and some do not. Here is a small list of examples:
Treasure Hunting - Gives lockboxes like slicing does. Also finds gemstones that are used in Armstech and Cybertech items, and may also be used in some Artifice items.
Investigation - Finds rare plastics used in creating armor for Smugglers, Agents, Sentinels, and Marauders. It can also find random schematics for any crafting skill.
Underworld Trading - Finds rare metals used in Armormech for Troopers, Guardians, Juggernauts, and Bounty Hunters. It can also find chemicals used in creating Biochem implants.
Diplomacy - All diplomacy missions give dark side or light side points. Some diplomacy missions give rare silks used by Synthweaving for force user armor.