We consider the massive star formation properties, radial profiles, and atomic gas masses of those galaxies in our Hα Galaxy Survey that have close companion galaxies, in comparison with a matched control sample of galaxies without companions. Our analysis is based on Hα and continuum images of 327 disk galaxies that form a representative sample of the local universe. We find that the presence of a close companion raises the star formation rate by a factor of just below two, while hardly at all increasing the equivalent width of the Hα emission. This means that although statistically galaxies with close companions form stars at a higher rate, they do this over extended periods of time and not as bursts. We find no significant increase in the central concentration of the star formation as a result of the presence of a close companion. The fraction of truly interacting or merging galaxies is very small in the local universe, at around 2%, and possibly 4% of bright galaxies. Most of these interacting galaxies currently have unremarkable star formation properties. We also study the properties of the galaxies in the survey with the most extreme values for star formation indicators such as rate, equivalent width, star formation rate per area, and gas-depletion timescale. We find that each of these indicators favors a different subset of galaxies, and use this information to discuss critically the possible definitions of the term starburst to describe galaxies with enhanced star formation activity. We conclude that no one starburst definition can be devised that is objective and generally discriminant. Unless one restricts the use of the term "starburst" to a very small number of galaxies indeed, the term will continue to be used for a heterogeneous and wide-ranging collection of objects with no physical basis for their classification as starburst. Our overall conclusions are that (1) whereas the rare interacting and merging galaxies may have enhanced star formation, and vice versa, those galaxies with the highest star formation are often interacting or merging, the influence of the presence of a close companion on the star formation in galaxies is in general very small, and long lasting; and (2) the term "starburst" cannot be easily defined objectively and generally in physical terms.