What is the difference between insecticides and pesticides?

"Pesticides" is a very wide category that includes, algaecides, herbicides, insecticides, bactericides, fungicides, etc.

If you look again at your primary link, it shows the descent in tabular form, i.e.

Pesticides
Insecticides

If carried further, it may look like:
Pesticides
Insecticides
Algaecides
Fungicides
Bactericides
Herbicide
s
etc

All of the above come under the FIFRA rules of the USEPA, requiring registration for any product CLAIMED to have pesticidal capabilities.

Sample page saved for reference:  http://www.hclrss.demon.co.uk/class_insecticides.html#botanical_insecticides

 

Compendium of Pesticide Common Names

Insecticides

Copyright 19952003 Alan Wood