What is the difference between "backhaul" and "core" network in cellular networks?
Let's have a little bit of a glimpse from the diagram below; 



What you can analyse in that diagram,is a convention point to point (PTP) and line of sight (LOS), a microwave link uses atail node and aggregation node,which allows remote base station to  access the core network through the backhaul link.

Therefore,backhaul network is a side network which communicates with the core network,i.e. it links packets to and from  the core network.

That said, cellphones also communicates with a single cell tower which constitutes a local network (subnetwork);whereby the link between the celltower and rest of the world(to the core network) begins with the backhaul link. The rest of the world is termed as autonomous network system,which is administered by global internet providers.

A high-level summary is that cellular backhaul refers to transport from remote cell towers to mobile telephone switching offices (MTSO). This backhaul is frequently provided by a third-party internet service provider via layer 2 circuits. The ISP's edge device (optical switch or router) with a customer handoff point (UNI) is located at the cell tower and the network demarcation between the ISP and the cell provider's core network (ENNI) is located at the MTSO. An EVPL (point-to-multi-point) configuration is commonly implemented with both circuits traveling from the tower to the MTSO over divergent paths to provide redundancy.

Hope this can give you some insights.