Remember that the OSI model is simply a model, and the real world doesn't always fit so neatly into it. There are many models, but none are followed completely.
The Data-Link layer is layer-2 under the OSI model. The addresses used by many (but not all, just the IEEE) LAN (layer-2) protocols are called MAC (Media Access Control) addresses. Hosts on a LAN using an IEEE LAN protocol (e.g. ethernet or Wi-Fi) communicate with each other using MAC addresses.
One major problem with the OSI model is that OSes never actually implemented separate layers 5, 6, and 7. That means that those layers are really lumped together in the Application layer, which is off-topic here.
The Application layer sends data to the Transport layer, where it is encapsulated in datagrams for transport. Some Transport layer protocols use source and destination addresses. For TCP and UDP, we call those addresses ports, and the TCP datagrams are called segments because the application data stream is segmented.
The Transport layer sends its datagrams to the Network layer, where the datagrams are encapsulated in Network layer datagrams, called packets. The packets have source and destination addresses.
The Network layer sends the packets to the Data-Link layer, where the packets are encapsulated into frames (MAC function). The IEEE Data-Link layer protocols use source and destination addresses, called MAC addresses, on the frames. Other layer-2 protocols may use other addressing, or none at all.
The Data-Link layer sends the frames to the Physical layer (hardware) for encoding of the frames where they are placed on the "wire".
The receiving host will reverse the process, decoding the bits on the wire into frames, which send their payloads to the appropriate Network layer protocols (LLC function), which then send the packet payloads to the appropriate Transport layer protocols, which send the payloads to the appropriate application processes.
Each layer on a source host communicates with the corresponding layer in the destination host, so, no, the upper layers are not skipped when two hosts on the same LAN communicate.
Understand that a host can have multiple Network layer protocols. The way the IEEE LAN protocol decides which Network layer protocol gets the payload of a frame is referred to as LLC. The actual encapsulation of network packets in frames is called MAC.
Don't make the mistake of thinking the whole world uses IEEE data-link protocols, although they are dominant on LANs. There are many different data-link protocols, and many do not use LLC or MAC, which are defined by IEEE 802.