Short term memory is one part of your memory system. Things come in through your senses and stick around from 1/4 second to 3 seconds in your Sensory memory. The useful data is then passed onto your short-term memory, where it is used. That data which is rehearsed will probably then pass on to your Long-term memory.
There is some debate as to how closely the two memories, short-term and long-term, are related. They may be almost the same thing, or they may be completely different. There is some evidence that everything passes into your long-term memory, and it is only problems with retrieval that keep you from using the information in long term memory in the same ways, and with the same detail, that you often can with short term memory. On the other hand, anterograde amnesia, which prevents you from encoding any new information into long-term memory, doesn't seem to have any effect on short-term memory, implying that there is a definite and important disjoint between the two.
Under the standard model, your short-term memory is made up of three components: the acoustic code, the visual code, and the semantic code. Acoustic is the weakest, often just rote rehearsal. Semantic is the strongest, and using this is the most likely to get info into your long-term memory. There is also a difference between maintenance rehearsal (rote) and elaborative rehearsal (playing with the idea)--elaborative stuff will get into LTM much easier. Without any of these rehearsal codes data in the short term memory will start to decompose in about 18 seconds.
It is often held that the STM can hold only about seven pieces of info before it starts dropping old ones*. This does not mean seven digits or seven words, this means seven of whatever units you are using. If you are remembering nine digits, '395676359' may overflow your short term memory, but '123456789' probably will not. (Units: 'nine numbers' and 'in order'). A unfamiliar telephone number may be seven separate chunks, but a familiar one will be one chunk ('John's number').
Short-term memory as a theory is being replaced with, or perhaps conjoined with, Working Memory.
AKA primary memory and active memory.
Clinicians, and in many cases, the general public, may use a different definition of short-term memory: short-term memory is memory for events which occurred recently (in the last few days or weeks), while long-term memory is memory for events which occurred in the distant past.
* Miller's Magical Number, brought to public attention by George Miller in 1956, is 7+/-2 (that is to say, from 5 to 9, depending on the person, the situation, etc.). He called the units of STM Chunks, and they are well known in psychology. People have complained that these chunks are ill-defined, and they may be on their way out.