There is another period of mourning during the Counting of the Omer. The difference between them is that mourning in the Omer has the status of minhag (custom) and in the Three Weeks it is din (law).
Both periods have to do with the destruction of the two Temples. In regard to the Three Weeks the link is perfectly obvious, for we suffered a horrific disaster when the enemy desecrated our sanctuary and set it alight. But what about the Omer period?
The popular explanation quotes the death of Rabbi Akiva’s large numbers of students without whom the struggle against the Romans was compromised, yet large numbers of Jews died as martyrs throughout out history and no prolonged periods of mourning were inserted in the calendar in their memory.
The difference is that the commemoration probably entered Jewish life no earlier than the Crusader era and the students of Rabbi Akiva became symbolic of pious, learned Jews who lost their lives because they would not abandon God and His Torah.