Please forgive my newbie questions.

I am homeschooling my two children, DD8 and DS5. They're both bright and ahead, but not off-the-charts academically gifted.

My son has always had quirks. We shrugged them off for years, said things like "If he didn't [make eye contact, display emotional empathy, etc], we'd totally think he was on the spectrum."

As he's getting older, his "quirks" are separating him more and more from his peers. I'm trying to decide whether to have him testing for ASD/Asperger's or Gifted, to have an idea of how to approach things with him and possibly to have access to more resources (our state provides financial help if they have an ASD diagnosis).

But I'm kind of lost. My husband and I both went through gifted testing in school (and were pulled out for the program), but I don't know how things work these days. Do I have to choose one and have him formally "tested"? Can I see someone and have them evaluate him for both?

Or maybe this is not outside the realm of "normalcy"? My daughter is the typical high-achieving good girl, so maybe it's just compared to her that I'm seeing his difficulties as abnormal?

His quirks:

[*] Obsessions/perseverances (As a toddler and preschooler, this was space, to the point where he would give friends tours around Kennedy Space Center at the age of 3 and 4. Parents in the homeschool co-op not-so-jokingly suggested he teach a space class. Now it's Minecraft, and he seemingly CAN'T talk about anything else. Seriously 90%+ of the sentences he utters in a day are about Minecraft.)
[*] Can't play with peers because he's too rigid (Trying to play x-wing/tie fighter with another boy, and my son was in tears because the boy wanted his tie fighter to have shields, but my son has read in books that they aren't equipped with shields.)
[*] Fixation on justice/following rules (He dislikes magicians because he sees them as "lying" to the audience.)
[*] This has gotten better in the last 6 months, but he can get "stuck" at the end of a word or sentence and repeat it over and over ("I built this Lego star fighter-fighter-fighter-fighter.......")
[*] Difficulty handling time stress (countdowns, timers)
[*] Difficulty transitioning away when he's involved in something
[*] Some noise sensitivity
[*] Some anxiety
[*] Lots of wiggling/movement (can't even sit down through dinner), but not to an AD/HD extent
[*] Well below average in writing
[*] But he's friendly and engaged with older kids and adults, learns quickly, reads well above grade level, make connections, and asks interesting questions

Thank you for any insight you can offer!