All bugs are insects; not all insects are bugs. True bugs are classified in the Order Hemiptera. A practical example may help to illustrate the distinction.
Dragonflies and damselflies — my first loves in the Class Insecta — are classified in the Order Odonata. They are insects but not true bugs. Make sense?

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)
Wheel Bug (Arilus cristatus) is a true bug in the Family Reduviidae (Assassin Bugs) that preys on pest insects. Notice the red proboscis below the head of the Wheel Bug — a non-retractable structure that is used to pierce and suck the life juices from prey.

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)
This is one crazy-looking bug — the “wheel” on its back reminds me of Stegosaurus!

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)

15 SEP 2016 | Huntley Meadows Park | Wheel Bug (Arilus cristatus)
Related Resource: All bugs are insects, but not all insects are bugs, a blog post by The DragonflyWoman.
Copyright © 2016 Walter Sanford. All rights reserved.