Darwinism: Evolution by natural selection (I find "survival of the fittest" a particularly misleading phrase - and it's not really used by those in the know anyway). The generally accepted use excludes some misconceptions Darwin had or didn't rule out [not having a handle on genetics at the time], including Lamarckianism, the fallacy that acquired characteristics could be inherited. However, this general use is more strictly neo-Darwinism (below)
neo-Darwinism: Not correctly in current use; refers to refinements of Darwinism to about 1895. Wikipedia redirects this to the following (modern evolutionary synthesis), although there is an extant article on neo-Darwinism if you have the link - here. Incorporates refinements from Alfred Wallace (often mentioned along with Darwin when books are in the mood to be more correct), which specifically exclude Lamarckianism.
Modern evolutionary synthesis: the general basis of evolutionary thought since the 1940s. Genetic variation happens through chance mutation (and recombination in sexual interaction/selection); evolution happens through changes in the frequency of alleles (variants within a species) between one generation and the next, through natural selection and genetic drift. You can see how Wikipedia puts it here.
There's some subsequent argument on the unit of evolution: is it the gene (Dawkins)? The individual? The Species? or the Clade? (Gould seems to argue for some combination or synthesis of these.)
Some books put together an equation, with many incomplete variants such as:
reproduction + natural selection + mutation = evolution
From my readings, I would add some attendant concepts that help round out conceptualisation of evolution.
anthropocentrism - the great barrier to clarity in understanding is our own location at this point in evolutionary time and space. We too easily see things to our own scale and bias. The path to modern human has been, as one writer said "zigzaggy" over a period of time that is impossible to properly place in perspective.
the environmental niche - that is, an environment and its attendant organisms, whether it is isolated or experience some movement in or out of the environment
genetic drift (as mentioned above) - that is, even aside from mutations that are more favourable within the environment, there are changes (mutations) that have no nett effect on the individual or species survivability within that environment. The smaller the population, the more prone to drift, where isolated from other members of the same species and even when the environmental niches are equivalent. Change still happens.
redundancy and multiple use - a great engine for evolutionary change is available when two body parts can fulfil the same function, or one part can serve two functions. For example, a swim bladder in a marine creature that eventually facilitates air-breathing and develops into a lung; or bones in the jaw that help perform rudimentary auditory functions, then over time become exclusively used for hearing.
environmental change - more of a fundamental than most people admit, in my reckoning. Even aside from catastrophes that result in mass extinctions, environmental niches are never static in geological time scales. The whole planet is not static: plate techtonics, over time, affect global and local environments.
On another note, it's too easy to pretend environments don't change, and that without human interference, the planet would be a happy little paradise of biodiversity. That's simply not true - on geological time scales. But on the time scale of human history, it's sad but true: we have rocked the boat far too quickly.