The autism comes first. Sensory needs; SID/SPD is one of the criteria required for a child to be classified as a child w/ autism.

The biggest thing to remember is that Autism is a syndrome.
In medical talk, a syndrome is a set of symptoms or signs that occur together and suggest the presence of a certain disease or condition. There are many syndromes and for each one, there is a list of symptoms or signs that people with that syndrome
might have.
Each condition has been assigned diagnostic criteria; to 'have' that diagnosis, the person needs to have a certain number of the signs and symptoms on that list. The diagnostic criteria might also include certain combinations (this particular signs
and these 2 particular signs must all be present to have the diagnosis).
The signs and symptoms themselves might be common in other conditions too - for example, Rett Syndrome, Autism, Asperger's Syndrome, ADD, OCD, SID, SPD (and a lot of other conditions) - all have a lot of the same signs and symptoms. It's fairly common for kids to have a diagnosis first given and later changed based on looking at the list again and seeing that they meet the criteria for a different condition later on.
Some syndromes have diagnostic tests that can be used to confirm the diagnosis. Downs Syndrome for example, used to just have a list of signs and symptoms that, present together, meant Down Syndrome. When it was discovered that there was a genetic 'marker' that showed DS, that became the test that confirmed it.
Since there is not any confirming test like that yet for Autism, all they have to go on is comparing the child's list of signs and symptoms with the list that is on the diagnostic criteria for Autism.
On the idea of spectrum, I've heard about a lot of conditions having a spectrum. People with Cerebral Palsy might be low on the spectrum with very mild CP that affects a few of their abilities. Or, they might be high on the spectrum, with severe spasticity. Any condition can be described like that - the more symptoms, the higher on the spectrum. Or, as was already said:
karynnix said:
When I talk to kids about autism, I tell them that the "spectrum" is like the color green. There are many, many different shades of green. With some shades, like hunter green and lime green, it's really easy to tell the difference between them. Some shades are so close that it's hard to tell them apart.
Autism is the only condition I have heard non-medical people use the word spectrum for. But, people (medical and non-medical) don't always use the term the same way. Some seem to use it for people who don't meet all the diagnostic criteria for autism ("He is somewhere on the spectrum" - which probably means something more like "He doesn't meet all the criteria, but he meets some and I think he has autism"). Some use it to talk about people who do meet the criteria for autism, but are using it to describe the shades of green that karynnix mentioned.