Shorten, curtail, abbreviate, abridge, retrench can all mean to reduce in extent, especially by cutting.
Shorten commonly implies reduction in length or duration. It is also often used of apparent rather than actual length.
Curtail adds to shorten the implication of making cuts that impair completeness or cause deprivation.
Abbreviate implies reducing by omitting some normally present or following part; thus one abbreviates a word by cutting out or cutting off letters; one abbreviates a discussion by bringing it to a close sooner than planned or anticipated.
Abridge expresses reduction in compass or scope rather more than in length, but it may imply the retention of all that is essential and the relative completeness of the result.
Retrench stresses reduction in extent or costs of something felt to be in excess.