das Paket
package / parcel
An item wrapped in paper or packed in a box that is sent by mail or courier service.
Der Postbote hat heute Morgen ein Paket für dich gebracht.
The mail carrier brought a package for you this morning.

package
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package / parcel
An item wrapped in paper or packed in a box that is sent by mail or courier service.
Der Postbote hat heute Morgen ein Paket für dich gebracht.
The mail carrier brought a package for you this morning.

Especially in Austria, instead of 'das Paket' (package/parcel), the diminutive form 'das Packerl' is often used in everyday language.
Ich muss heute noch ein Packerl zur Post bringen.
I still have to take a small package to the post office today.
In connection with mail shipments, 'Paket' (package/parcel) is often used with the verbs 'schicken' (to send), 'bekommen' (to receive), 'annehmen' (to accept, when it is delivered), or 'aufgeben' (to send/drop off at the post office).
Hast du mein Paket schon bei der Post aufgegeben?
Have you already sent my package at the post office?
In a figurative sense, 'Paket' (package) refers to a bundle of measures. It is often used in compound words such as 'Maßnahmenpaket' (package of measures), 'Rettungspaket' (rescue package/bailout package), or 'Gesetzespaket' (legislative package).
Die EU hat ein großes Rettungspaket für die Wirtschaft geschnürt.
The EU put together a large rescue package for the economy.
You can recognize the figurative meaning from the context. Words like 'Regierung' (government), 'Gesetz' (law), 'Wirtschaft' (economy), or 'Finanzen' (finances) indicate that a bundle of measures is meant.
Das neue Gesetzespaket wurde im Parlament diskutiert.
The new legislative package was discussed in parliament.
program / shipment
'die Sendung' and 'das Paket' can both mean something that is sent. 'Paket' is a concrete item, usually a box or something wrapped, that you receive by mail. 'Sendung' is more general and can include a package, several packages, letters, or goods. The words are easy to confuse because a package is often a shipment. If you mean the individual box, 'Paket' is more natural; if you are speaking generally about shipping or the goods being sent, 'Sendung' fits better.

Meine Mutter bringt morgen ein großes Paket zur Post.
My mother is taking a large package to the post office tomorrow.
Die Sendung aus dem Online-Shop ist noch nicht angekommen.
The shipment from the online shop has not arrived yet.