The larger the iron, the larger the curls which will be created.
Irons with 2 or 2 1/2" barrels - which are hard to find - will create very loose curls. The larger the size of the section of hair you curl, the looser and larger the curls. The smaller the size of hair which is curled, the tighter the resulting curls.
Irons with 1 or 1 1/2" barrels - which are the most common - will create medium sized curls. The larger the section of hair, the looser the curl. The smaller the section of hair, the tighter the curls.
Irons with 1/2" inch barrels will create much tighter curls, especially when used on small sections of hair.
The smallest irons with barrels that are 1/8" or 1/4" or 3/4" sized barrels are small enough to curl the sections of hair all the way to the roots of the hair. The larger barrels won't be able to reach directly to the roots.
Curling iron barrels are a lot like hair roller sizes. Big curlers & big barrels create big results. Small curlers & small barrels create small results. The amount of hair you wrap around either curls or curling irons will also have an impact.
Tightly curly hairstyles require small barrel irons, big loose curls, waves & loose ringlets require medium to big irons.
Hope that helps.