The difference I found between AMF and MME selection is that LTE eNodeB considers load factor of each MME in the group MME group and based on load factor eNodeB selects MME for a new UE message i.e. Initial UE message. In the case of 5G-RAN node, it selects AMF not only based on load factor of each AMF in AMF pool, it also considers Networks Slice Selection Assistance Information (NSSAI).
In 5G network, AMF is the entity which is responsible for Access and Mobility management of 5G devices. There is a concept of network slicing and each network slice consists of set of AMF, SMF and UPF.