Last Activity Time refers to the time when changes are made to a record, whether it is adding a note, closing a task, sending emails or just editing the fields.
Last Modified Time will only capture changes made to the fields and does not include changes made to the Notes, Tasks or Email sections.
For more details on the activities, please refer to this link: https://www.zoho.com/crm/help/reports/generate-reports.html#Use_%27Last_Activity_Time%27_in_Criteria