A package is something that you pack and send out. If you order something online, you are ordering a package. If something gets sent to your house (that comes in a box or bigger container) you are being sent a package.
A packet typically refers to a group of papers stapled together. A teacher can hand you a packet of homework or you can be given a packet of documents.
To pack is the verb used for putting something into a container. If you’re going on vacation, you’ll have to pack a suitcase. If you want to send your friend a gift, you must pack the gift.
Hope this helped! :)