What is the difference between a martyr of this world (shaheed al-dunya) and a martyr of the Hereafter (shaheed al-akhira)? And is someone who dies in an accident while on their way to deliver a lecture for their work considered a martyr of this world?

One who dies in an accident while going to work is not considered a martyr of this world (shaheed dunya), because a martyr of this world is one who is killed in jihad for a worldly purpose. However, he may be among the martyrs of the Hereafter if the conditions for attaining martyrdom are met, such as death by an abdominal illness, being crushed by a falling building, drowning, or plague.