you get crumbly, lumpy and clody soil structure, when the soil is mechanically 'disturbed' - by tillage or ploughing, by action of soil organisms (e.g. high earthworm activities favour a crumbly soil structure; moles, voles, pigs etc. digging in the soil), by shrinking/swelling of clay-rich soils, by wind-thrown trees....
In the FAO guidelines (Table 48, p.46) it reads: Crumbs, lumps and clods: Mainly created by artificial disturbance, e.g. tillage.
The difference is the size, whereas crumbles are smallest and clods are the largest fragments. All three types of soil structure occur only in the topsoil.
Crumbly soil structure can also be naturally induced in soils with high activity of soil organisms (e.g. earthworms) - the mineral particles are stabilized by humus, algae, bacteria and fungal hyphens. Crumbly structure in the topsoil is most favourable for plants.
Lumpy aggregates can be found mainly in ploughed topsoils (together with crumbly structure). They have sizes up to about 50 mm.
Clody soil structure you can find in fine-grained topsoils which are ploughed in wet conditions.
In the "Field Handbook for Describing and Sampling Soils" (v2) by the USDA-NRCS they say for clods:
Artificial earthy fragments or clods: Irregular blocks created by artificial disturbance, e.g. tillage or compaction. "Cloddy" used only to describe oversized, "artificial" earthy units that are not pedogenically derived soil structural units; e.g., the direct result of mechanical alteration (use Blocky Structure Size criteria)