das Programm
program
A planned sequence of content, performances, or broadcasts, for example on television, radio, or at an event.
Was läuft heute Abend im Programm?
What’s on the program tonight?

program
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program
A planned sequence of content, performances, or broadcasts, for example on television, radio, or at an event.
Was läuft heute Abend im Programm?
What’s on the program tonight?

You can recognize the exact meaning of 'Programm' (program) from the context. Words like 'Fernsehen' (television) point to a broadcast, 'Computer' to software, 'Partei' (party) to a plan, and 'Waschmaschine' (washing machine) to an operating mode.
Ich muss noch schnell ein Programm auf meinem Laptop installieren.
I still need to quickly install a program on my laptop.
In the context of events or media, typical phrases are 'auf dem Programm stehen' (to be on the program) or 'im Programm laufen' (to be shown / to be on the schedule).
Heute Abend steht ein interessanter Dokumentarfilm auf dem Programm.
An interesting documentary is on the program tonight.
In connection with software, 'Programm' (program) is often used with verbs such as 'installieren' (to install), 'starten' (to start), 'ausführen' (to run), 'schließen' (to close), or 'deinstallieren' (to uninstall).
Bitte schließe alle Programme, bevor du den Computer ausschaltest.
Please close all programs before you turn off the computer.
When referring to plans by organizations, 'Programm' (program) is often combined with verbs like 'vorstellen' (to present), 'beschließen' (to decide on), or 'verabschieden' (to adopt).
Die Regierung hat ihr neues wirtschaftliches Programm vorgestellt.
The government presented its new economic program.
With household appliances, verbs like 'einstellen' (to set), 'wählen' (to choose), or 'starten' (to start) are used to select a program.
Für diese Wäsche musst du das Woll-Programm einstellen.
For this laundry, you need to set the wool program.
project
'das Programm' and 'das Projekt' can both have to do with planning and organization. But they do not mean the same thing. 'das Programm' often describes a sequence of items, for example at an event, on television, or as an organization's plan. 'das Projekt' is an undertaking with a goal that people work on for a period of time. Learners may confuse the words because a project can have a program. Remember: the 'Projekt' is the task or undertaking; the 'Programm' is more the sequence or the planned content.

Mila sieht in der Pause das Programm für das Schulfest an.
During the break, Mila looks at the program for the school festival.
Wegen der neuen Straße hat die Chefin dem Projekt mehr Zeit gegeben.
Because of the new road, the boss gave the project more time.