Equal shares of identical wholes are the same size.

The square on the left is partitioned into two same size shares, or two halves.

The square on the right is partitioned into two shares which are not the same size; it is not partitioned into halves.

The square on the left is partitioned into four same size shares, or four fourths.

The square on the right is partitioned into four same size shares which are not the same shape. It is also divided into four fourths.