Azure Managed Disk are used as block-level storage volumes that are managed by Azure and used with Azure VMs (It will be stored as a .VHD file). You have 3 options, Standard HDD/SSD, Premium SSD and Ultra Disks.
Azure File offers fully managed file shares in the cloud that are accessible via SMB protocol. Azure File shares can be mounted (attached) by both on-premises and cloud machines. Also, applications can mount a file storage share to access file data, just as a desktop application would mount a typical SMB share.
I hope this answered your question.
Best regards!
F.