Larry Culp’s first shareholder letter as General Electric Co.’s CEO was relatively brief and deployed less frequently some words and phrases that longtime leader Jeff Immelt often used to define the goals of the once-sprawling conglomerate.

The shorter missive reflects changes in GE itself, which has had three CEOs in three years, can only afford to pay a token dividend and is breaking itself apart. The company lost some $200 billion in market value over two years and was dropped from the Dow Jones Industrial Average last...