Layer 2 handles traffic at MAC level so just above the physical layer, while Layer 3 is more complex. You can read more here.
It would be useful to consider the whole OSI model and how layer 2 and layer 3 fit into it.
The network layer provides the functional and procedural means of transferring variable length data sequences from a source to a destination via one or more networks, while maintaining the quality of service requested by the Transport layer. The Network layer performs network routing functions, and might also perform fragmentation and reassembly, and report delivery errors. Routers operate at this layer—sending data throughout the extended network and making the Internet possible. This is a logical addressing scheme – values are chosen by the network engineer. The addressing scheme is hierarchical.
The best-known example of a layer 3 protocol is the Internet Protocol (IP). It manages the connectionless transfer of data one hop at a time, from end system to ingress router, to router to router, and from egress router to destination end system. It is not responsible for reliable delivery to a next hop, but only for the detection of errored packets so they may be discarded. When the medium of the next hop cannot accept a packet in its current length, IP is responsible for fragmenting into sufficiently small packets that the medium can accept it.
Simple answer: Layer 2 works with the Data-Link Layer and MAC addresses / Broadcast domains. Layer 3 is the Network Layer and works with IP addressing and Routing…
A number of layer management protocols, a function defined in the Management Annex, ISO 7498/4, belong to the network layer. These include routing protocols, multicast group management, network layer information and error, and network layer address assignment. It is the function of the payload that makes these belong to the network layer, not the protocol that carries them.
The data link layer provides the functional and procedural means to transfer data between network entities and to detect and possibly correct errors that may occur in the physical layer. Originally, this layer was intended for point-to-point and point-to-multipoint media, characteristic of wide area media in the telephone system. Local area network architecture, which included broadcast-capable multiaccess media, was developed independently of the ISO work, in IEEE Project 802. IEEE work assumed sublayering and management functions not required for WAN use. In modern practice, only error detection, not flow control using sliding window, is present in modern data link protocols such as Point-to-Point Protocol (PPP), and, on local area networks, the IEEE 802.2 LLC layer is not used for most protocols on Ethernet, and, on other local area networks, its flow control and acknowledgment mechanisms are rarely used. Sliding window flow control and acknowledgment is used at the transport layers by protocols such as TCP, but is still used in niches where X.25 offers performance advantages.