By definition, a neurotransmitter is any specific chemical that crosses a synaptic space after being transmitted from a presynaptic cell, and acts on a post-synaptic cell. By "specific", I mean the chemicals that are neurotransmitters belong to the following classes: Amino acid, Amine, Peptide. Histamine, when secreted from a neuron (pre-synaptic), to act on another neuron, or the one that secreted it (post-synaptic), is called a neurotransmitter. But it is also produced and secreted by mast cells. When released, histamine acts on cells other than neurons; therefore it is not acting as a neurotransmitter.
A hormone is a substance that is secreted by an organ or part of the body, into the blood stream, and is thereby transported to another body part (or it may act on the organ that secreted it), to illicit an action. Endocrine glands secrete hormones, but not all hormones are secreted by glands. For example, secretin is a hormone, but is secreted in the gastrointestinal tract by CELLS. Note also, that not all hormones are proteins; they can be peptides, steroids, amino acids and derivatives of catecholamines.
IN GENERAL, hormones are substances that are secreted by glands and travel through the bloodstream to reach their target cells which can be anywhere in the body, and neurotrasmitters are substances released from the axon terminals of neurons and cross a very small intercellular gap and bind to receptors on the adjacent cell: both hormones and neurotrasmitters communicate information and affect their target cells.
There are exceptions. For example, it turns out that a lot of structures that we don't think of as glands secrete hormones: adipocytes, the heart, and the skeleton are examples.