These four terms have caused confusion in the prepress, design and printing industry for as long as they have existed. Often they are used interchangeably, but each one does in fact have its own meaning.
Firstly, the acronyms stand for the following:
DPI, Dots Per Inch
LPI, Lines Per Inch (often called Line Screen)
PPI, Pixels Per Inch
SPI, Samples Per Inch
PPI and SPI are the easiest to define, as the meaning almost is interchangeable. PPI refers to the numbers of pixels an image has per inch, in both the X and Y direction. So 92PPI means there will be 92x92=8462 pixels in a one inch square. SPI means exactly the same thing, only PPI is used to refer to an image on screen, whereas SPI is used when scanning a document, i.e. taking a ‘sample’.
Essentially PPI and SPI refer to the resolution of an image on a computer rather than on a physical item.
DPI and LPI are a little more confusing. DPI is most commonly used when referring to the resolution of a digital printer. For example a typical office printer may claim it is capable of printing up to 1200DPI resolution. Considering the average lithographic printed sheet is printed at 175LPI, 1200DPI sounds a lot, but in reality it means very little.
An inkjet printer basically sprays ink onto a page in a relatively disorganised fashion. The higher quality printers also use different dot sizes to achieve better colour reproduction and the DPI value states how many of these more or less randomly placed dots appear in an inch on the paper. So 1200DPI means there are 1200x1200=1,440,000 dots printed in a single inch of the printed sheet. The same goes for laser printers, only with a different method of applying the ink.
LPI refers to lines per inch and does not have an equivalent in digital printing terms. When printing lithographically, the dots of ink on the printed sheet have a very exact placement. They are usually oval shaped and each colour is printed at a different angle to the other on the sheet to avoid artefacts. On a 175LPI job, there are 175 of those lines across each inch. However, when printing lithographically there is still a DPI value involved. While there may only be 175 lines per inch, there will in fact usually be 2400-3000 dots per inch. Each dot in the 175 lines per inch is actually made up of dozens, or hundreds of even smaller dots that give the DPI value. The number of these dots defines how many different shades are possible to achieve per colour, for each larger dot (in the 175LPI).
For example you may have a 200LPI job printed using only 200DPI, but you would need to use tricks to achieve the appearance of more than one shade of the colour (let alone the ~256 that is normal).
DPI is for the most part ignored in lithographic printing, LPI is the value that matters and DPI will generally be set as high as the plate making machine allows. Although technically as LPI increases you get less shades available per dot, the way the plate is made gives the visual impression that this is not the case.
The two rules most commonly used for creating artwork for printing are either:
a. Always create images at 300ppi or
b. Always create images at double (some say 2.2x) the desired LPI (or the LPI specified by the printer).
In reality, to achieve a good result, it is fine to use an image with the same PPI as the LPI it will be printed in. The standard of using 300PPI simply came about because 300LPI was the highest commercial lithographic printing typically went to. It also means that if the job will only be printed at 175LPI and the artwork needs to be modified by the printer, they can do so while still keeping enough detail to print properly.