lomography is blanket name for a style of photography using retro and basic cameras, the most prominant example of which bieng the lomo.
Lomo was a russian brand of camera, with the famous 'holga' model (which is actually 120film, but can be adapted to 35mm) and the Lomo-LC compact models.
Other models are the diana and the horizon.
The ethos is pretty much point, shoot and see what you get, there are seldom any focus controls, apertures are limited and on the holga, pretty much ineffective. The cameras have major abberations such as edge darkness and softening (called vignetting) and are known to leak light.
It all gives carefree happen chance results.
35mm film is a small format film based on early motion picture film, but with the axis rotated 90 degrees for a larger frame area, popularised by the Lieca brand. 35mm format offered great results for low cost and because the film is smaller the cameras are more portable.
Lomo shooters are known to use out of date film and cross processed film (slide film put through print developer) which adds to the overall effect -more saturated colours, sometimes very unrealistic colours.
Lomo is a brand name, and a generic style.
I prefer a decent SLR and can add most of the lomo effects later in post. With a lomo you are stuck with the effect, and the novelty can wear off quickly.
That said, I had a horizon 202 which I loved to bits.