A standard is any shrub trained into the shape of a tree, with a single trunk. See Tree Roses, a synonym for rose standards.
[From A Year of Roses, by Stephen Scanniello, pp. 146-147:] Tree roses, also called standard roses, are often displayed to their best advantage when planted in containers... Tree roses come in heights anywhere from two feet high (most common with miniature roses) to over six feet. There are two forms of standard roses available. One if the common form of a long stem supporting a bushy display of roses, sort of like a large lollipop. The other is a weeping standard, the only style I think worth using.

Tree roses are created by attaching three buds of a rose cultivar to a long straight stem of another rose. The most common stem stock to use is an unnamed rugosa rose variety. Other roses have been used for creating standards, but the rugosa seems to be the strongest, surviving the longest.

Standards can include three different roses: a rootstock, a standard understock, and a scion, which is the rose you see. The standard understock should be a tough rose that does not sunburn. Some producers of standards will use a proprietary standard stock. De la Grifferaie is used for very tall standards, but because it sometimes suckers from the roots, it is budded to a rootstock. Baileys recently patented and released Polar Joy, a hardy standard rose that is the same rose, roots, standard, and scion, and tip hardy to Zone 4.