Chromatin state refers to the marks (i.e. methylated DNA, histone modifications, euchromatin v. heterochromatin) found at specific loci and is often referred to as open (readily bound by DNA binding proteins, like transcription factors) or closed (inaccessible to most factors).
Chromatin interactions can include the binding of transcription factors and other DNA binding proteins, but is usually used to describe local and long distance functional contacts between two or more regions of chromatin. These interactions are generated actively through protein-dependent chromatin organization and passively via polymer physics and the nuclear environment.
Chromatin structures can refer to the actual molecular shape and composition of the DNA or to the molecular modifications found at specific regions of chromatin (e.g. heterochromatin, DNA methylation). It can also refer to the ordered compaction of mitotic/meiotic chromosomes.
Chromatin loops are structures that may act in promoting regulatory interactions. Conversely, chromatin interactions may induce looping.
Cavalli and Misteli, Functional Implications of Genome Topology, Nature Structural and Molecular Biology 2013