Vesicles and vacuoles are sacs used for storage inside eukaryotic cells. Plant cells have a single vacuole which is generally the largest organelle inside the cell. In animal cells, there are several vesicles which are smaller and more numerous than vacuoles.
When scientists first looked through microscopes, one of the things that they first noticed especially in plant cells is that it looked like there was this big empty thing. And so they were looking and going "big empty thing" but it's actually, we know we just they're looking through microscopes and its actually small, so they called it a little empty thing. That keeps in before and words like vacuum which means an empty space, so vacuoles are just membrane sacks inside of a cell and just similarly there's smaller versions of vacuoles called vesicles. Both of these membrane sacks are used for storage of materials. Now the larger ones called vacuoles are typically used to store things like water and food while the smaller ones called vesicles are often used to contain or store things neuro-transmitters the chemicals used to communicate between a neuron and some other cell or they're used to transport materials from one location in the cell to another.
If we take a look over here at a plant cell you can see this large structure here is the water vacuole. Generally a plant will help inflate its cell by pumping water into the one central vacuole that it has, so in a plant cell, you'll easily be able to spot the water vacuole its this big thing right there and in fact they had to shrink it to make fit in this diagram cause usually it is the largest structure that you'll see.
In a plant cell, or sorry in a animal cell you'll see lots of little sacks, all those could be vacuoles perhaps they're storing some food or some starch or whatever, sometimes they may be smaller ones that are already filled with various chemicals and so if they're moving around they're generally considered to be vesicles and that's it so vacuoles and vesicles they're just sacks, the big difference is scale.