When electrons move, free of the nuclei of atoms, and there is a net flow, this flow is called electricity, or an electric current. This might be compared to a flock of sheep moving north together, while the shepherds do not.
So-called "static electricity" is not a flow of electrons at all. More correctly called a "static charge", it refers to a body that has more or fewer electrons than are required to balance the positive charge of the nuclei. When there is an excess of electrons, the object is said to be "negatively charged". When there are fewer electrons than protons, the object is said to be "positively charged". When the number of electrons and the number of protons are equal, the object is said to be electrically "neutral".
The electron is one of a class of subatomic particles called leptons which are believed to be fundamental particles (that is, they cannot be broken down into smaller constituent parts).