All the 36 Arizona wheat, rye, and barley grasses and their allies are in the tribe Triticeae and all are rather similar, looking like the seedheads advertised on wheat cereals. Most have awns and are sessile spikes. Rye is an annual grass that most often holds its seedheads upright until they start to dry, at which time they tend to nod. Its smooth green leaf blades can be half an inch wide. Seedheads can be six inches and the entire plant can grow to 10 feet tall.
Cereal rye is made easier to identify by thousands of years of selective breeding. As a result, its spikelets and especially the florets holding the seeds are extra large and plump. Winter wheat (Triticum aestivum, shown here) looks quite similar to Rye, and it also escapes cultivation. There are wheat varieties that are awnless, but many farmers prefer the awned variety, so both are common and easily confused with rye. I find that wheat spikelets are even plumper than rye.