The wording here is purposefully confusing. While a packet technically refers to layer 3, it is a common misnomer for "data transmitted on a network." It is uncommon to hear someone say a frame was transmitted, simply saying packet is much more common. A switch will receive a packet with a frame inside it, and transmit the entire packet using the frame's MAC address.
A network switch (also called switching hub, bridging hub, officially MAC bridge) is a computer networking device that connects devices together on a computer network, by using packet switching to receive, process and forward data to the destination device. Unlike less advanced network hubs, a network switch forwards data only to one or multiple devices that need to receive it, rather than broadcasting the same data out of each of its ports.
A network switch is …