I assume those are both WISC-Vs and not -IVs. Has any professional discussed extended norms with you? Your child clearly attained max subtest scaled scores on at least four subtests (both VCI and both FRI) on the second administration, which suggests that the index scores are low estimates. And that the Index differences may actually be much wider than they already appear to be.
And from what I can see, the VSI subtests were pretty consistent within the cluster, (as were, obviously, the VCI and FRI subtests) which suggests that the VCI/FRI > VSI difference is real. Which leads me to the construct of nonverbal learning disorder, which, while not a formal diagnosis in the DSM or ICD, can have some utility in understanding certain profiles where language-based skills are much stronger than visual spatial/nonverbal skills. I bring this up not to stick another label on, but because there is a fair amount of overlap between the presentation of persons on the autism spectrum and persons who could be described with the NVLD model. In this case, of course, this would be more of a relative weakness (or strength, in the other direction!). There is a long-standing discussion based on clinical observations regarding NVLD vs ASD, as both may involve some subset of: rigidity/resistance to change, anxiety, difficulties with reading social situations (or face-blindness), and executive function challenges. The principal distinction would be in the presence or absence of theory of mind (perspective-taking), and in how that contributes to differences in social perception. It is hypothesized that in NVLD, misreadings of social situations occur because of relative weaknesses in visual-spatial perception-- difficulty perceiving the visual cues that help NT observers interpret social behavior. In contrast, in ASD, difficulty reading social situations arises from limitations in theory of mind/perspective-taking. The visual cues are accurately perceived, but the observer does not automatically respond to the emotions with which they are usually associated. (Side note: some interesting research on mirror neurons, in this context and others.)
If we were to consider an application to your DC's case, it would be to discuss whether what the school perceives as ASD-ish is some of the social and emotional presentation often associated with NVLD-type profiles. Remember that there is no core social comprehension deficit in NVLD. Just relative weaknesses accurately reading nonverbal communication at speed, and the sequelae of those misperceptions. So it's not incompatible with a happy, social, outgoing child, especially when in relaxed, familiar environs.
BTW, the high energy may sometimes be related to the profile, too, because less efficient processing of visual spatial input means that less incidental environmental sensory stimulation is making it into the system, which can lead to stimulus-seeking behavior (aka, high activity level). It's not unusual for this profile also to be misdiagnosed (and sometimes mis-medicated) as ADHD.
If you feel comfortable posting subtest scores, we can see if there's anything more to be gleaned from them, but from what I can see, unless there's a marked difference within the WMI or PSI (e.g., at least 3 scaled scores), or inside the Digit Span component scores, that's probably not necessary.
