Yes and more
Stye is a general non-medical term used by non-ophthalmologist describing generally any pimple like lesion of the eyelid.
Most people do interchangeably use stye for hordeolum
and chalazions. Hordeolum and chalazion
, are same except hordeolum usually appears red and painful, suggesting an infection. Chalazion are not red or very painful. Either can be internal or external.