The radio-sensitive emulsion of radiographic films consists of silver bromide (AgBr) grains suspended in gelatin. Depending on the film type, the grains have different shapes and typical sizes / diameters between 0.1 and 3 micrometer.
Radiochromic films don't contain such grains, that is why they are called "grainless". But the radio-sensitive layer of radiochromic films consist of a monomer (that gets polymerized when irradiated), which also has an inherent structure in micrometer scale.
Both radiographic and radiochromic films have a very high spatial resolution for measuring dose distributions compared to other types of radiation detectors, such as ionization chambers, scintilation or semiconductor detectors, or TLDs.
But I still have a doubt. Like you said, "the monomers in the active layer of radiochromic film have an inherent structure in micrometer range" then, how come they are grainless? What exactly is responsible for the high resolution of these films?
From the links I sent you saw the microscopic images of both radiographic and radiochromic films. As I said, the characteristic of being "grainless" refers to the missing metallic silver or silver salt grain. The terms "film grain" or "granulariy" comes from photography, where the grains are really visible inside the images (you will find some explanations e.g. at Wikipedia). Radiochromic films do not content such grains, instead they have a (hair-like) monomer structure. But this monomer structure is typically not refered as "grain" as, in addition, it is also not visible inside the image. So it is more or less a problem of terminology, since both radiographic and radiochromic films do have some kind of an internal structure...
Spatial resolution is limited by the internal structure of the films (grain / monomer size) but also by the way of film handling / evaluation (magnification, type / resolution of scanner, etc). A resulting dose distribution can be measured in steps of several micrometers. Other types of radiation detectors (e.g. ionization chambers, scintilation or semiconductor detectors, TLDs) have typical sizes /diameters in millimeter range resulting in a lower spatial resolution. To measure in small steps, you need to travel these detectors (which is hard in micrometer range), but the radiation field will always be influenced by the detector itself. This effect is also minimal for the thin film layers.