What is the difference between Asperger Syndrome and ASD Level 1?

No. It was once the dividing line between 'high functioning autism', with speech delay, and Asperger's, without speech delay. If they are using DSM-5 ASD, they really need to read the diagnostic criteria contained in it and not just invent stuff. No-one now gives diagnoses of Asperger's, it is all ASD (or ASC). The criteria they are quoting do not exist for diagnosis of ASD Level 1. Diagnostic criteria are summarised as: “persistent difficulties with social communication and social interaction” and “restricted and repetitive patterns of behaviours, activities or interests” (this includes sensory behaviour), present since early childhood, to the extent that these “limit and impair everyday functioning”.  Nowhere does this include delay in speech and language acquisition or low academic achievement. At best the school are putting their own limits on to whom they give support and passing this off as being clinically sanctioned. At worst they are entirely uninformed about ASD diagnostic criteria. Presumably, there is  no-one at the school who is qualified to give a clinical opinion? In which case their criteria are invalid anyway.

A clinical assessment would be the best thing for the child. In the meantime there are a number of AQ tests for autistic traits available online, getting scores within the autistic range might give some leverage over the school.

The level accompanied by the diagnosis is no more than a suggested level of support given by a professional who diagnosed you with autism. It's often no longer used as the levels doesn't stay consistent through autistic individuals life as certain life events, comorbid disorders and age all affect the ability to function causing inconsistencies in support required. 

support levels are being phased out of the diagnosis process as support level 1 was mistakenly given to autistic females as they tend to camoflauge, mask and fake social skills hiding the severity of issues during autism assessments. The leveling system also was abused by medical professionals & social support services as the term high functioning was replaced with level 1 autism spectrum disorder which was used to refuse support or assistance because the vagueness in the diagnostic manuals and literature.

Schools across england have Special Educational Needs Co-ordinator who are supposedly qualified in learning disabilities and neurodivergence and are qualified to make referrals with parents permission to pediatricians & Medical professionals. Unfortunately Special Educational Needs Co-ordinator are limited by funding restraints set by local authorities and schools in the meantime before an autistic child gets official diagnosis schools often have to fork out their limited funding on support for the a single child. the local authority often refuses to backdate or reimburse the schools on money spent on providing additional support and will only start giving the school funding the day in which a child receives a diagnosis which can range from anything from a few months to several years which schools are hesitant on doing. This often means children who are academically gifted or are able to just get by are potentially ignored or purposely overlooked. Sometimes you'll find the school will throw them into special class with a single teaching assistance to thirty students to save money.  

which means schools actively discourage the Special Educational Needs Co-ordinator making referrals for that exact reason.                

The level accompanied by the diagnosis is no more than a suggested level of support given by a professional who diagnosed you with autism. It's often no longer used as the levels doesn't stay consistent through autistic individuals life as certain life events, comorbid disorders and age all affect the ability to function causing inconsistencies in support required. 

support levels are being phased out of the diagnosis process as support level 1 was mistakenly given to autistic females as they tend to camoflauge, mask and fake social skills hiding the severity of issues during autism assessments. The leveling system also was abused by medical professionals & social support services as the term high functioning was replaced with level 1 autism spectrum disorder which was used to refuse support or assistance because the vagueness in the diagnostic manuals and literature.

Schools across england have Special Educational Needs Co-ordinator who are supposedly qualified in learning disabilities and neurodivergence and are qualified to make referrals with parents permission to pediatricians & Medical professionals. Unfortunately Special Educational Needs Co-ordinator are limited by funding restraints set by local authorities and schools in the meantime before an autistic child gets official diagnosis schools often have to fork out their limited funding on support for the a single child. the local authority often refuses to backdate or reimburse the schools on money spent on providing additional support and will only start giving the school funding the day in which a child receives a diagnosis which can range from anything from a few months to several years which schools are hesitant on doing. This often means children who are academically gifted or are able to just get by are potentially ignored or purposely overlooked. Sometimes you'll find the school will throw them into special class with a single teaching assistance to thirty students to save money.  

which means schools actively discourage the Special Educational Needs Co-ordinator making referrals for that exact reason.