What is the gel-like material inside the cell and inside organelles called?
It depends on the cell and/or organelle under question.
Generally, "gel" in cells is termed cytosol, commonly confused with cytoplasm, which merely describes what's "in" the cell, including organelles.
"Gel" in chloroplasts is termed stroma, which takes part in photosynthesis. To be sure, when photosystem II is producing ATP, a proton gradient is formed between the thylakoid's lumen (e.g. w/in the sac) and the stroma. An enzyme called ATP synthase facilitates diffusion of protons out of the thylakoid, coupling the kinetic energy of this process with the endergonic process of ADP phosphorylation.