As near as I can make out blind survey refers to a survey that is not a set of aimed observations of previously known objects (galaxies, stars, clouds), but is attempting to discover unknown sources and/or gather statistics that avoid some of the inevitable bias.
Such a survey often covers a pre-chosen region of the sky, and deep surveys often fit the description. It may cover a larger survey field, even to the extent of being labeled all sky, but there are obvious trade-offs regarding angular resolution, signal strength, wavelengths covered, and amount of the celestial sphere covered.
Some surveys termed "blind" aim at a particular volume, e.g., the Milky Way, or a redshift range, and/or aim at a specific phenomena, such as pulsars, or the 21cm line at different redshifts. Some transient surveys have been described as "blind", and the term seems to fit many of them.