Will all the music played by piano work well in a keyboard?
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Most music for piano will also be possible to play on a keyboard. How different the experience will be, really depends on your keyboard. It is also a question of your preferences and needs.
Here are some important differences to consider:
Number of keys
Many keyboards will have fewer keys than a piano. See this question for good answers to what you will lose with fewer keys (61-key keyboard vs 88-key piano). For most musical pieces this will not be a problem, but there are some composers that has written pieces that use the full extent of the 88-keys (see the previous link for examples).
What you normally call "keyboard" will often not have weighted keys, which means you lose some dynamic in volume and intensity. You do have digital pianos that have weighted keys, which gives a natural feeling and dynamics control, but this is not so common in keyboards. A digital piano is designed to have a more natural sound and to feel like a real piano, but it is also more expensive. See this question for some good answers to how having weighted keys influences your playing and sound.
Keyboards come in all price categories, and of course you will see big differences in the most expensive vs. the cheapest. The more expensive, the better the sound is usually the general rule here. If you aim for the most natural piano sound and feel and are willing to spend money, you should go for a digital piano, which are more expensive than most keyboards.