How are the plants in these pictures properly spaced (details)?

Plants in pots are usually annuals, meaning that they will give you glorious blooms for the summer (or their blooming season, depending on what your growing zone is.)

That is very different from planting perennials in the ground, where they will be a permanent, or almost permanent, part of your garden. The root systems need room to grow both down and out; hence the warning not to crowd.

Each spring you put new soil, food and plants into a large pot, place in sun or dappled shade according to the plant’s particular need, water and enjoy. After the first frost, you dump the whole thing into your compost.

Some plants also cooperate better than others. Most contemporary gardeners ignore this fact. Look in the wild: plants don’t always give each other space, but often grow wonderfully. Some fill different niches and therefore don’t compete with those they’re near. Some draw up nutrients that the others require. I’m growing corn, beans, and squash together in the traditional style; the corn enjoys the nitrogen from the beans, the beans trellis up the corn stalk, and the squash leaves keep the sun from drying the soil and keeps some pests out. Synergy.

My guess is that either those display plants cooperate/tolerate each other, or they’re basically not going to last.

Many arrangements from florists even include plants with drastically different water/light requirements (eventually, you have to take them apart if you expect them to survive).