I experience both. Shutdowns are generally from long-lasting overwhelming experiences - being in a busy or crowded place, for example. I become very tired and sluggish, I struggle to focus, talk or do much at all. I've been told by my husband that I move in slow motion. It takes me a long time to get out of a shutdown - or a sleep!
My meltdowns are caused by what I'd call 'bombardment', though that isn't strictly true. It's where I'm already struggling and then people are asking me questions, and they want answers, or there are things I'm expected to do, and I just can't cope with it all. In public I just get flustered and make a quick getaway, then go into a shutdown once I'm 'safe', but at home where I'm already in a safe space, they're (thankfully rare) occurrences where I will explode for just a few seconds (and then usually cry with the guilt of it afterwards).
The meltdowns occur at times when my husband is asking questions, and I'm struggling to work out my answers, and he keeps asking or he's talking whilst I'm thinking, or coming up with suggestions that are distracting me when I'm trying to work things out in my head. And I'm not angry, but I just need a break and I feel like I'm backed into a corner and trapped - it's a fight or flight thing. My husband used to think it was angry shouting, but I'm not like that at all. I am very rarely angry. I think he's only heard my anger twice, and whether he realised it or not, he did know the difference. These times were both pre-diagnosis, and both times he said "I've never heard you THAT angry before". The reality was that he'd never heard me AT All angry before.
Meltdowns aren't anger. They're panic. They're trying to force words out when they're stuck, so that they come out sounding loud and aggressive. I've had to explain to him the difference, but he still doesn't always get it. He'll occasionally comment that he doesn't understand why I'm angry about something when he was 'just trying to help'. I have to try and explain that there's no anger, and I know he was trying to help, but in listing suggestions when I'm already overwhelmed he just adds further blocks to an already wobbly tower, until it all falls down in a crash for a few seconds. As soon as I've 'snapped', I recover. Then, of course, I feel terrible. Thank goodness they're rare.