"Include" vs "involve": usage and difference

The first thing to say is that English has very, very, few true synonyms - if the word is different, there is a difference, at least, in the nuance.

When looking for the differences, there is not much point noting the similarities.

To involve has the literal meaning of "to be wrapped up in" or to be bound in".

To involve something indicates that the object or action takes an inseparable/integral part.

"The experiment involves the use of acid." -> "the use of acid" is an inseparable/integral part of the action of the experiment.

To include merely means that the object is contained within the greater group or whole. The literal meaning of "include" means "to be enclosed within something."

The package with the equipment for the experiment included a letter for Professor Brown.

You will see that something that is involved is also included, but something that is included need not be involved.