Team Members on Forge are legally W2 employees of the companies who decide to hire them on the Forge software.
On Forge, "approving" a Team Member means that a Team Member has completed the interview and training process, has completed all necessary paperwork associated with being hired and has been accepted to work at your company.
While there is no legal difference between hiring and approving a Team Member, the terminology "approved" is used to portray the idea that working for a company can sometimes be a fluid transaction. Take, for example, a college student who works for a restaurant near her college campus but comes home every summer and picks up a job at the local deli. The deli shouldn't have to "fire" and "re-hire" that college student each summer, instead, the college student should be "approved" to pick up shifts when she arrives back in town.