Mohammad,
The concept of an Alternate port was introduced with Rapid Spanning Tree. This feature takes over what the traditional (802.1 D) spanning-tree enhancement of “uplink-fast” used to do. The Alternate port serves as a “hot-standby” for a switch’s Root Port, but Alternate Port is considered to be in a Discarding state (Discarding is the RSTP term for Blocking, Listening, and Disabled for spanning-tree).
This means that an Alternate port can receive BPDUs but will not send them. As soon as a Root Port fails, the Alternate Port will immediately transition to forwarding, skipping the Learning state (there is no such thing as “Listening” in Rapid Spanning Tree).
You are correct that Root and Designated ports both send and receive BPDUs.