Difference between "packet", "parcel" and "package"

Solution 1:

Mostly conjecture and original research:

A parcel has the modern connotation of being sent by mail, and you normally never hear of the noun used to describe anything else (though you may sometimes hear it in verb form, meaning "to deliver in regular, divided amounts"). The word originated from the Old French parcelle meaning "a small piece or part".

A package also generally has the same connotation. The word evolved from "pack" which has its roots in Old German, to basically mean "the product of packing" similar to the etymology of "baggage". While a package is often sent by mail, you could hear of a "package" being stored, or of a "gift-wrapped package" being delivered in person.

A packet is a newer word, with forms first appearing in the 1500s (vs the 1200-1300s) in Middle French (pacquet). The word originally meant "bundle", but now typically has one of the following connotations:

• A small envelope containing spices, grain, seed, or similar material.
• A collection of papers or other information, often bound, as in the written material for a presentation.
• A chunk of data sent over a network.

Solution 2:

It is whatever you define it to be.

For the Post Office in the UK, a packet is generally smaller than a parcel though larger than a letter. Both a packet and a parcel might be informally called a package.

Solution 3:

There are connotations about shape and size in regards to the difference.

In regards to US English (as I am unfamiliar with British English): Typically, a packet is of a smaller scale than a parcel or package. You might put a packet of sugar in your coffee, or pick up a packet of papers at back to school night. Parcel or package would not be suitable in those contexts. Usually a packet would refer to an envelope shaped container with an assortment or quantity of materials or supplies inside, papers or flyers, sugar, peanut butter, salad dressing, etc.

In the US, parcel is almost exclusively used to refer to packages sent by US Mail, eg: their package sending service is called "parcel post" and is for sending boxes, or packages, of various sizes. Typically a US speaker would say package rather than parcel unless they are talking about how their item is being shipped. Package would connotatively imply a box or similar container with item(s) inside, usually not envelope shaped, usually it refers to a box-shaped item. As the other commenters have noted, the usage of parcel vs package is slightly different.