Your comparing apples and oranges but I get the sense you need a good description of both and you will be able to see they are worlds apart.
In short the big difference is the psychosis and typical onset time and a whole host of different lesser symptoms.
There no longer is an Asperger's Syndrome it has merged into all the Autism Spectrum Disorder ASD in DSM 5. I don't think there is cause to cite the entire DSM-5 on ASD.
ASD is something which is present and symptomatic from birth. Generally ASD may occur amoung those with high,average and low IQ. When it appears in the low IQ range their social functions are more hindered than another person with the same IQ. Essentially it is when a person lacks in social communication and social interaction like me. We have difficulty expressing reciprocity and engaging in normal conversation. Sometimes our micro-expressions are entirely different and we are incompatible with your micro-expressions. We act incorrectly in some social situations because our abilities to pick a mode are different. Sometime we have trouble making friends other times we just don't care about what our peers think. Repetitive to the point one might think its OCD. Specifically my repetition is fixing things. This becomes a problem when people come to me for help because I attempt to give them advice while pertinent they do not have the ability to follow because thier psychology doesn't allow the radical changes in response to corrections that mine does. Some repetitions are motor movements like Gary from the television show Alphas. It is my opinion that the DSM-5 over exerts itself when mentioning idiosyncratic phrases as that is much too overly broad. Those with ASD sometimes follow a specific ritual and must have everything around them be the same. I honestly don't know if I have a ritual. I seem to handle massive changes well as long as I have my computer and a net connection. I do ok without a net connection and a digital device but its not fun. The DSM really shines when it mentions rigid thinking patterns. As every ASD I've met has prescribed methods we follow. We are very predictable and generally have answers for many possible questions given a specific time to generalize other rules to the situation. In my case this becomes really fun when combined with religiousness as I can tell if I would consider something sin or even ethically right or wrong a mile away. Again like OCD restrictive focused fixations to the option of extreme expertise on a subject matter. I tend to fixate on different things at differnt times. I grow board of a subject or I'm no longer welcome to discuss such a topic then I move on to another. Like for a while it was Religion with Computer Science and Math, then Bioinformatics, then Psychology with Biochemistry and now Psychology with Device and Application development. So my fixations are not extremely restricted but they do honestly prevent me from doing anything else except those topics. Some ASD are very sensitive to sensory input. I'm not like that so I have no ability to give input. So again Gary could sense EM fields it is said that that actually exists with sound its called Chromesthesia. Gary could detect miniscule changes to the em field of the environment around him.
The severity of ASD is determined by its interference with your life.
ASD isn't directly chemically treatable but the anxiety is treatable with medication.
All things Schizophrenia and Psychotic disorders are more well defined and have a larger section in the DSM-5. It would be impossible for me to paraphrase the entire Chapter on Schizo type and psychosis based behavior. So we will just stick to the basic citation from the Schizophrenia itself diagnosis criteria.
Diagnostic Criteria 295.90 (F20.9)
A. Two (or more) of the following, each present for a significant portion of time during a 1 -month period (or less if successfully treated). At least one of these must be (1 ), (2), or (3):
Disorganized speech (e.g., frequent derailment or incoherence).
Grossly disorganized or catatonic behavior.
Negative symptoms (i.e., diminished emotional expression or avolition).
B. For a significant portion of the time since the onset of the disturbance, level of functioning in one or more major areas, such as work, interpersonal relations, or self-care, is markedly below the level achieved prior to the onset (or when the onset is in childhood or adolescence, there is failure to achieve expected level of interpersonal, academic, or occupational functioning).
C. Continuous signs of the disturbance persist for at least 6 months. This 6-month period must include at least 1 month of symptoms (or less if successfully treated) that meet Criterion A (i.e., active-phase symptoms) and may include periods of prodromal or residual symptoms. During these prodromal or residual periods, the signs of the disturbance may be manifested by only negative symptoms or by two or more symptoms listed in Criterion A present in an attenuated form (e.g., odd beliefs, unusual perceptual experiences).
D. Schizoaffective disorder and depressive or bipolar disorder with psychotic features have been ruled out because either 1 ) no major depressive or manic episodes have occurred concurrently with the active-phase symptoms, or 2) if mood episodes have occurred during active-phase symptoms, they have been present for a minority of the total duration of the active and residual periods of the illness.
E. The disturbance is not attributable to the physiological effects of a substance (e.g., a drug of abuse, a medication) or another medical condition.
F. If there is a history of autism spectrum disorder or a communication disorder of childhood onset, the additional diagnosis of schizophrenia is made only if prominent delusions or hallucinations, in addition to the other required symptoms of schizophrenia, are also present for at least 1 month (or less if successfully treated).
Schizoid Personality Disorder
Diagnostic Criteria 301.20 (F60.1)
A. A pervasive pattern of detachment from social relationships and a restricted range of expression of emotions in interpersonal settings, beginning by early adulthood and present in a variety of contexts, as indicated by four (or more) of the following:
Neither desires nor enjoys close relationships, including being part of a family.
Almost always chooses solitary activities.
Has little, if any, interest in having sexual experiences with another person.
Takes pleasure in few, if any, activities.
Lacks close friends or confidants other than first-degree relatives.
Appears indifferent to the praise or criticism of others.
Shows emotional coldness, detachment, or flattened affectivity.
B. Does not occur exclusively during the course of schizophrenia, a bipolar disorder or depressive disorder with psychotic features, another psychotic disorder, or autism spectrum disorder and is not attributable to the physiological effects of another medical condition. Note: If criteria are met prior to the onset of schizophrenia, add “premorbid,” i.e., “schiz oid personality disorder (premorbid).”
All things Schizo involve psychosis. Schizod being in cluster A makes it of type psychotic. They chemically treated with varying degrees of success even the negative symptoms and social problems.
So there is criterion F for Schizophrenia and criterion B for Schizoid personality disorder validate your question. Which points out that there is some overlap with ASD however the primary features of Schizo are the psychosis induced oddness so the overlap is minimal save social abilities.