Both plant and animal cells conain organelles such as mitochondria,endoplasmic reticulum, golgi apparatus, lysosomes, and peroxisomes and the nucleus but they have different needs. Plants need chloroplasts - necessary for photosynthesis - whereas animals do not.
Plant and animal cells are both eukaryotic cells and contain similar membranes, cytosol, and cytoskeletal elements. It is the cell membrane that controls what enters and what leaves cells.