What's the difference between an animal cell, a plant cell and a bacterial cell?

There are a few differences that you can use to tell apart or describe these types of cells.

The first distinguishing feature is whether the cell is eukaryotic or prokaryotic - this helps to separate bacterial cells from animal and plant cells.
Eukaryotic cells have a nucleus, and they usually combine into multi-celled organisms (i.e. plants and animals).Prokaryotic cells do not have a nucleus, and they exist as single-celled organisms (i.e. bacteria).
You can always differentiate a bacterial cell from an animal or plant cell, because the bacterial cell will have free DNA and plasmids instead of one round nucleus.

The second group of distinguishing features involve separating plant cells from animal cells. These cells do have a lot of structures in common (like the nucleus mentioned above) but a plant cell will have a few extras:
A cell wall - a rigid outer layer, often shown as being more of a square shape in diagrams.A vacuole - a fairly large area within the cell which contains sap (water and dissolved sugars).Chloroplasts - structures which carry out photosynthesis, often coloured green in diagrams.
These structures can always be used to tell if a cell is a plant cell.

There are other structures that these cells have in common (like the cell membrane, cytoplasm, and ribosomes) but because these are common to different types of cell, you shouldn’t use those to decide what type it is. Here is a simple thought process diagram to use: