A prokaryotic cell (bacteria, cyanobacteria) has no true nucleus and no membrane-bound organelles. Its DNA is a single circular molecule lying free in the cytoplasm in a region called the nucleoid. A eukaryotic cell (animals, plants, fungi, protists) has a nucleus with an envelope and organelles such as mitochondria, ER and Golgi apparatus.
Plant and animal cells are both eukaryotic, but plant cells have a cellulose cell wall, plastids and a large central vacuole, while animal cells have centrioles.
Cells are studied with microscopes. Resolution, the ability to show two close points as separate, matters more than magnification. Electron microscopes resolve far more detail than light microscopes.