What are the differences between ASD and ADHD, and some distinct aspects of the latter so I can understand if it could be affecting me?

There can be some comorbidity / overlap, but they're different things.

ASD - typical presentation includes difficulty interpreting facial expressions / vocal tone / figurative speech, difficulty with theory of mind or modelling the experience of others, difficulty with social protocols or cues, inflexible, literal interpretation of rules, sensory issues, overload issues, single-subject fixation, spatial perception issues.

ADHD - typical presentation includes difficulty ignoring distractions, dificulty remaining focused on non-stimulating tasks, poor executive function, poor time management, poor task management, poor emotional regulation, forgetfulness, impulsivity, rejection-sensitive dysphoria, sensory/overload issues, fidgeting.

It's possible (and quite common) to have both; it's also quite possible to have the same behaviours for different reasons. For instance, ASD people may fidget/etc as stimming to manage sensory overload, whereas ADHD people may fidget out of excess energy. ASD people may act in socially-inappropriate ways because they don't understand (or care about) the relevant social cues; ADHD people may act in socially-inappropriate ways because they've been distracted out of the context and find it difficult to moderate their interaction. An ASD person might stay up all night reading about some topic because they're kind of obsessed with it; an ADHD person might stay up all night reading about it because hyperfocus kicked in and holy crap it's 8am where did the night go?

ASD people I've known have described it as their magic telepathy helmet being broken and trying to make sense of utterly irrational-seeming other people; I'm ADHD and would describe it as my mental whiteboard being broken and living in a soft rain of post-it notes with every random observation written on them, whether relevant or not.

So, if I'm an adult who has never been diagnosed with either/anything, but I do all of the things you listed for ADHD and some of the autism ones... Should I be evaluated?
- As thebannanaking has said, for sure seek out help if you are struggling. I think that is the big indicator as to whether they will diagnose you. The symptoms have to be prevalent in your life. Personally if it helps put it in perspective, I've kind struggled most my life, a whole lot of fail if i am going to be honest. no clue why, never even thought about adhd until my boss literally sat me down after I almost got fired like 6 months ago and listed out a whole crapton of what I later found out where adhd symptoms. I've been struggling real bad lately with not just work but pretty much all areas of my life and so now I'm trying to navigate our crappy Healthcare system and get help. Better late than never I guess. So really what I'm trying to say is if you are having problems please seek help. Don't be like me and not deal with it for way to many years.
- I can't speak for the ASD side, particularly, but the relevant question for ADHD is whether it's impacting your quality of life.
  
  Are your studies suffering because you just can't make yourself hit the books? Are you constantly fucking up at work and putting your career at risk? Is sensory overload a major impediment to coping with existence? Are you concerningly unreliable with parenting stuff? Does grocery shopping take three hours because you need a handful of separate trips for all the things you forgot each time?
  
  If it's crossing over into disability territory, if life is just not supposed to be this hard, definitely get evaluated.
  
  If not, if it's just quirky and occasionally frustrating - ehh. It can be affirming and a definite relief to have a label to put on things, but it probably won't make a huge difference day-to-day. If you're in the US where medical bills are a major thing, take that into account.
I'm ADHD and I definitely fidget to manage my internal stimulus overload. If there isn't enough external stimulus happening my internal "noise" can become unmanageable and I end up fidgetting/stimming to help anchor me.
This is exactly the response I was hoping for, thank you so much, getting a little emotional reading both of them as, yes, there is overlap, but both present in me strongly. It gives me some hope that if I can ever get sorted for some medication for ADHD (if diagnosed), it may help my quality of life (I need things to look forward to in life or everything is a depressing hell).

Realistically, no-one here is qualified to give you an answer on whether you might have it or not.

That's something you might want to bring up to a psychologist or a doctor, although some ASD/ADHD organisations might have tests for whether you might have something worth checking out.

As a head-start, you might want to look into the RAAS-D, and the ASRS, which are qualified tests to gauge the possibility of you having either ADHD or ASD. You could bring them in to show your doctor, and go from there.

Thanks, I'm not looking for a diagnosis, just signs which I can look for. I don't have the option of getting diagnosed sadly.

They are often interlinked and you can have both, many people do. The best thing to do is to get evaluated for it.

That's not possible so I'm asking about the aspects which are clear for you so I can understand better.

What I have been told by a psychiatrist (and don't completely agree with) is that unless you're trying to get medication to treat symptoms, it doesn't matter which one you have / get diagnosed with. The non-medication treatments are the same for both.

I'm sorry I don't have a more helpful answer. Sometimes things are more connected than we'd like, and we can't always separate them.

I've recently started taking medication to reduce the frequency of my migraines. I'm still not sure if it's done anything for the migraines, but it's had the side effect of making my ADHD symptoms more manageable. I really wasn't expecting that.

Your migrane medication tends to have stimulants to increase it's efficacy (usually caffeine), I guess it's enough for ADHD symptom management
- While that's true for over the counter migraine meds which are usually just an NSAID or Tylenol with caffeine, I suspect OP is referring to the preventative RX medication you take every single day and takes a long time (months, irrc) to see if it has any improvement. Which is why it's interesting that it helps! I wonder if that's a known benefit.
  
  Also OP hope it helps with your migraines too! They are horrific. And if you're able and need a rescue/acute med when you do have please talk to doctor about if triptans would work for you. Not recommended for people with Aura headaches or on SSRIs but they work great if you can take them.

As someone who has recently started the diagnosis journey and who is yet to be actually diagnosed, reading things like this I'm curious (and a little anxious) about how a professional is likely to interpret my experiences.

For example, I have no problem interpreting facial expressions or gauging the mood of a group of people, but I do find myself getting hung up on explicit/literal interpretation of rules, I get fixated on a single subject, and I do get overloaded as soon as I walk into a situation with more than one activity to focus on.

However, I also have issues ignoring distractions, focusing on non-stimulating tasks, forgetfulness and fidgeting.

I'm curious what peoples' experiences are with symptoms that cross (I guess, for lack of a better phrase) "fields of diagnosis"?