What is the difference between canthopexy and canthoplasty and when and why does a plastic surgeon perform either?

Canthopexy is a lessor procedure that uses a suture to reinforce the lateral canthal tendon. Canthoplasty is a reconstruction of the tendon that cuts the tendon from its bone insertion, shortens the tendon and reattaches it to the orbital rim. Canthopexy is often done as an additional step to support the lower eyelid at the time of lower eyelid surgery to avoid a pulled down lid.  It is often insufficient when the eyelid is markedly lax and does not have the power to correct lid malposition. The canthoplasty is a much stronger procedure but also more complicated. There are many variations on these procedures and no real studies to guide surgeons when to use one approach over another. Most eyelid surgeons who are not fellowship trained oculoplastic surgeons do not perform lateral canthoplasty.

in the canthopexy the same lower cruciate is ligated not cut. This procedure usually is used in patients with severe horizontal laxity of their lower eyelid. It can be combined with lower eyelid blepharoplasty or can be done by itself to improve the laxity of the lower eyelid, horizontally. 

Canthopexy and Canthoplasty are basically the same thing when they relate to lower eyelid blepharoplasty. They are used to tighten the outside corner of the lower eyelid to try to avoid ectropion (an excessively low position and sometimes a turned out appearance of the lower lid). This is not always necessary in lower lid surgery. It is generally needed more often if a large amount of skin is removed or the patient has a weak lower lid such as with a poor "snap" test result. The "snap" test is pulling the lower eyelid away from the eye and watching how fast is returns to the original position. In general, older patients have weaker lower lids and are more likely to need a canthal tightening if lower eyelid surgery is done.  Thank you for your question.