Autism is now defined in the DSM-5 as a single diagnosis of Autism Spectrum Disorder (ASD) that includes Asperger's Disorder (AD), High Functioning Autism (HFA) and so on. Anyone with a well-established DSM-IV diagnosis of these is effectively 'ported' into the ASD diagnosis - but people who would previously have been diagnosed with AD or HFA might not now meet the criteria for ASD, which is recognised to be an oddity or anomaly. A key reason for the porting principle is that DSM diagnoses are sometimes closely linked to service-provision and funding (particularly in the US) and it was clearly undesirable for people to run the risk of losing needed services. The ICD still retains a variety of different diagnoses (with somewhat different criteria to the DSM) - but it does note that Asperger Syndrome is of uncertain classificatory validity.
With dyslexia, it is important to understand that it is not a consistently formalised diagnosis to start with - with quite different definitions in the two main diagnostic systems (i.e. the DSM and ICD). It does, however, have a meaningful definition, adopted by the BDA following the influential Rose report, in that it describes specific problems with individual word reading and/or spelling. It must just be noted here that this means that dyslexia, according to this definition, is therefore not directly related to handwriting, verbal comprehension, maths, numbers and so on - and that if you can adequately read and spell individual words, you do not have dyslexia. This is the only definition that properly accounts for the idea that problems with individual words are not due to general intellectual ability: if reading comprehension is included in dyslexia (as the ICD does), it becomes very difficult to see how that is different from general intelligence even though we know that people with quite low intelligence can usually develop good individual word reading (because the brain systems related to the processing of individual words and their sounds develop quite independently from those responsible for other things like reasoning).
What has then happened with the use of these diagnostic labels is of some real importance. On the one hand, dyslexia has come to be used to describe almost any sort of literacy disorder regardless of whether it involves word reading and/or spelling - which is the ICD approach. It is therefore used with little reference to the underlying issue of whether someone can read words. This would seem to undermine the very idea of dyslexia as a specific learning disorder and results in it losing any clear meaning.
On the other hand, autism (or, specifically, ASD) has become more restrictive as a diagnosis, at least in the DSM system. Greater awareness of autism has meant that it is now more likely to be assessed for - but it seems that this is often on the basis of an assessment 'for ASD' rather than a proper neurodevelopmental assessment that results in whichever diagnoses are appropriate. It is unfortunately common that children with quite evident problems are not given any diagnosis because they do not meet the current DSM criteria: when this occurs, it can only be described as a failure to understand the diagnostic process, which requires that a diagnosis is given whenever there is evident sustained impairment.
Quite why the use of these diagnoses has gone down these paths is far from clear. It may well be because (i) different professional groups tend to make the diagnoses, with dyslexia assessments being largely done by Educational Psychologists and autism being mainly covered by medics of various sorts and (ii) the wider awareness of dyslexia preceding that of autism has somehow affected the ways in which people think about them (e.g. that dyslexia is relatively common whereas autism is rare).
Whatever the reasons, the key issue is that both dyslexia and autism are just a small part of the broad range of neurodevelopmental problems people can experience. We know that those problems tend to cluster together in various ways - and that there are some exceptions to this, like speech sound processing, which can be impaired in relative isolation. Diagnoses are really just a way of carving up the issues into meaningful clusters: they do not determine the nature of human experience or somehow define what is possible in terms of neurodevelopment; they are merely an attempt to systematically classify particular common groupings of symptoms.