Process is used to describe the fibres spreading from the cell body of a neuron; both axons and dendrites.
Dendrites are the processes that convey information from the postsynaptic terminals, normally towards the cell body of the neuron. Many types of neurons have numerous dendrites spread around the cell body, each of which branch to form hundreds of synaptic connections, receiving input from multiple presynaptic cells; this is called the dendritic field, AKA the dendritic tree.
Axons are the fibres that carry information to the presynaptic terminals, normally from the cell body of the neuron. Most neurons only have one axon that carries information away from the cell body, but that axon may bifurcate (split) to carry information to two different nuclei (areas) within the brain and/or may branch at it's destination to form multiple synaptic contacts with neurons in the same area.
Axodendritic Processes are a little more complicated! Some neurons form presynaptic and postsynaptic terminals on the same processes, therefore these neurons only convey information over short distances and may help to spread a signal within a small area.