"Direct" suggests costs can be traced to products, responsibility centers,
etc. "Variable" means costs vary with a cost driver such as volume.
These concepts are not equivalent (although the terms may be used interchangeably in
practice)! For instance, fixed costs can often be traced and thus can be properly
labeled as "direct." A common example of confusing these concepts occurs
when managers are not willing to layoff direct labor in a downturn. This results in
direct labor behaving like a fixed cost -- at least in the short run. (Common
economic justification for this practice is the need to retain a pool of skilled
employees.)
The Moral? Traceability does not automatically imply variability!