both plant and animal cells have the nucleus. The plant cell is made of cytoplasm, chloroplast, nucleus, cell membrane and cell wall. The animal cell is made up of the nucleus, cell membrane and cytoplasm.
A bacterial cell has no nucleus. It is prokaryotic, meaning before nucleus, whereas a plant cell has a nucleus and is eukaryotic, meaning true nucleus. Also, plant cells are often specialized whereas bacterial never are.
If a cell does not have a nucleus, then it is a prokaryote. If a eukaryotic cell has chloroplasts, then it is a plant or algal cell. If a cell has a nucleus but no chloroplasts, then it could be an animal cell.