It may be that the stains on your worktop are concentrated into the high traffic areas (ie. areas where you work most often) or they may be general and widespread across the whole of your worktop. If the stains are general and widespread across the whole of your worktop, there is little doubt that a full re-sand and re-finish will work out more effective and more efficient, both time and cost-wise.
That said, if you only have random stains here and there, you should be able to tackle these and remove them effectively without going to the extent of a complete re-sand and re-finish. Generally speaking stains on worktops fall into two categories: surface and deep.
Most surface and deep stains are caused by trapped moisture. Generally speaking if the stain is white, it’s only on the surface, if it’s black or dark, it has had a chance to penetrate deeper into the wood.