Nuclear batteries are generally self contained, single-use electrical power sources, typically with lifetimes of decades, but with low power outputs, based on decay of radioactive isotopes. As such they are not nuclear reactors as they do not involve either fission or fusion reactions.
Radioisotope Thermoelectric Generators use decay heat to drive electricity generation (and also as a heat source directly on some spacecraft).
Electricity can be harvested directly from beta emitters, such as the much-hyped nuclear diamond batteries.
Thermionic emission can also be used as a source of electricity, where electrons are boiled off a hot metal surface (known in electronics as a cathode) and collected on another electrode (the anode). According to Atlas Energy Systems, who claim to be working on such devices:
The process of thermionic conversion has been known for almost 100 years but it was not until the 1950s that it was pursued seriously. At that time the US and the former Soviet Union began extensive development of thermionic nuclear reactors for space due to the technology’s high reliability, compactness, and power density. This research culminated in the flight of two, fully operational 5kW electric thermionic reactors by the Soviet Union in the late 1980s. However, with the termination of space nuclear power programs in the 1990s, much of the thermionic converter development halted completely and the technology never found a foothold in terrestrial applications; despite being proven extensively in combustion-fired and concentrated solar systems.
In a video (below) from the 2017 Thorium Energy Alliance Conference Atlas's founder and CEO Ian Hamilton describes work on batteries based on what sounds like a different principle he describes as using "a plasma to convert ionising radiation from any isotope into electricity"