These say two different things.
The most tuna are caught in early November.
This means more tuna is caught in early November than any other comparable time frame. Here, 'most' is a superlative meaning "the amount that is greatest". It means the quantity of tuna caught in early November is greater than anything comparable, which would be tuna caught during other comparable time frames.
Most tuna are caught in early November.
This means that the majority of tuna that are caught are caught in early November. Here, 'most' is an intensifier meaning "more than half".
So, for example:
The most births occur in August and September
This is true, more births occur in those months than any other comparable time frame.
Most births occur in August and Septmeber.
This is false. In fact, most births occur in the other 10 months.