Es werden fleißig Päckchen gepackt.
Sie packen Geschenke ein.
- Es werden fleißig Päckchen gepackt.
- Es werden fleißig Päckchen eingepackt.
1 means: You are wrapping something (let's say books) into paper, and the result of that process are packages.
Before: Books plus packing paper; the books are not inside the paper. There are no packages visible.
After: All books are wrapped in packing paper. You'll see no books, just packages.
2 means: You already start with packages and wrap them into another layer of packing paper.
Before: Packages (let's say that are all red) plus packing paper (which we believe here to be green); the red packages are not wrapped into the green paper.
After: Green packages. (If you remove the green paper you find red packages; if you remove the red paper, you'll find the content)
- Sie packen Geschenke.
- Sie packen Geschenke ein.
Sentence 3 has no clear meaning. It says, that they are packing something, and the result of that packing are gifts. Most people will understand, that the results are packages that are meant to be gifted to other people. But this is not exactly what this sentence says. You better should not build such sentences.
Sentence 3 could also mean: You try to arrange gifts to fit together into a container. But in this case you'd better add an information about that container to the sentence, like:
Sie packen Geschenke in den Kofferraum des Autos.
They pack gifts into the cars luggage space.
Sentence 4 says: They have gifts, and they have packing paper, and they wrap the paper around the gifts to turn them into packages.