Generalizing/simplifying: Transmission is long distance - high voltage, think steel towers with wires.

Distribution is from a local transformer (substation) where high voltage gets turned to lower voltage (12 kV) and then sent via utility poles to your home. Near your home there will be a utility pole with a transformer that brings the voltage down to 110. You share that transformer with a handful of neighbors.

Your answer is good. To add to it, the large "transmission" grid usually covers extremely high voltage lines: 115 kV, 138kV, 230kV, 345kV, 500kV, 765kV and up. It is managed by both utilities and RTO/ISO organizations that manage large sections like air-traffic controllers. Distribution is typically below ~100kV and is really more in the 11kV range and managed by the utilities almost exclusively. Building new transmission lines can be ~$1 billion projects.