My experience with co-advising is that it most tends to emerge from some combination of the following circumstances:
- The student's project has some sort of interdisciplinary nature, such that the "primary" advisor does not have the ability to entirely supervise the student on their own at a technical level.
- The advisors have a very close collaboration already, such that it is natural that a student working for one is de facto working for both.
- The "co-advisor" is effectively the primary advisor, but cannot technically be so for various reasons, such as not being a primary investigator or being at a different institution (academic or otherwise).
Any or all of these may pertain at once. In essentially all cases that I have been familiar with, however, the supervision is of a single project, not of different projects for different advisors.
Funding most typically comes from the primary advisor (who usually would not have taken on the student without having the ability to fund them), but individual circumstances can lead to any number of other arrangements.