Yes depending on the procedure being perform , the size of the speculum used changes. For example procedures like colposcopy , IUD, Cervical and Uterine Biopsies, large speculums are used to visualize the area or to afford /accommodate the instruments used for the procedure. Even for routine PAP you may need to use a larger, longer , narrower, speculum depending on the patient's anatomy.
As previously mentioned , generally women who are virgins or not given birth traditionally have small to medium speculum used , whereas women who have given birth have medium to large speculum used. However the extent to which it can be open also plays a part as you don't need to fully open and lock the speculum in situ .
Choice of speculum either metal or plastic depends on the procedure as well , procedures like LEEP ( Loop Electrosurgical Excision Procedure ) traditionally used a metal speculum , but with the cost of autoclaving. Plastic is fast becoming the standard , as it's cheap and single use.
The type of speculum used also to some extent is determined where you live, traditionally in the US they use either Graves , Pederson or Cusco's speculums. In the UK it's been Collins speculum traditionally , but now it seems to be Cusco's speculums ( plastic ) due to cost.
Hope this helps
RN