Both have Latin roots similar to the English, and the big clue here is the prefix "pre-" meaning before, in advance, prior. In latin servare means "to keep safe" and the total effect of the prefix and the root is "action done in advance to maintain or protect."
Conserve can be a synonym of preserve. The prefix "con-" or with added to the root intensifies the meaning of servare, however it does not imply the added sense of "an action done to keep safe."
To preserve an object is to protect it from change. To conserve an object, on the other hand, is to use an object sparingly with the knowledge that it could run out.
In terms of food...
In the sense that to conserve means "to maintain as is," conserved food, in this case fish, could refer to a certain type of fish that has been maintained as a food source against over-fishing or something like that. Preserve, in the sense of "maintain for the future," would refer to fish that had been cured and packaged so that it could be eaten at a later date. The curing and packaging would be the proactive safeguard.
There is some overlap here, but I think, in the case of food, the difference between conserved food and preserved food is the difference between food that has been served in limited quantities and food that has been put in the freezer for later.