Understanding the interactions between nanoparticles (NPs) and biological matter is a high-priority research area because of the importance of elucidating the physical mechanisms underlying the interactions leading to NP potential toxicity as well as NP viability as therapeutic vectors in nanomedicine. Here, we use two model membrane systems, giant unilamellar vesicles (GUVs) and supported monolayers, to demonstrate the competition between adhesion and elastic energy at the nanobio interface, leading to different mechanisms of NP- membrane interaction relating to NP size. Small NPs (18 nm) cause a "freeze effect" of otherwise fluid phospholipids, significantly decreasing the phospholipid lateral mobility. The release of tension through stress-induced fracture mechanics results in a single microsize hole in the GUVs after interaction. Large particles (>78 nm) promote membrane wrapping, which leads to increased lipid lateral mobility and the eventual collapse of the vesicles. Electrochemical impedance spectroscopy on the supported monolayer model confirms that differently sized NPs interact differently with the phospholipids in close proximity to the electrode during the lipid desorption process. The time scale of these processes is in accordance with the proposed NP/GUV interaction mechanism.