Yeah, they're not strict terms. I personally think a significant differentiator though is that "homelab" tends to have a bit more emphasis on, well, the lab part. Ie., there is a certain amount of experimentation going on with some regularity. Beta software and firmware or even hardware, bleeding edge stuff, a higher tolerance for breaking things (and maybe leaving them broken for a bit when something else catches one's eye), etc. Some of the stuff attempted might not have any direct work requirement or value. It might be purely for fun and personal learning, and/or it might have some professional relation in terms of testing out new stuff in a initial way and kicking the tires before any kind of initial serious deployment. I mean, again there are certainly no hard and fast rules, but "homelab" settings often place more emphasis on dynamism than pure reliability, such as virtualizing things one normally wouldn't all on a single box. Virtual routing/firewall/edge and NAS are big examples to me that normally have their own dedicated hardware (be it on the metal or virtualized as part of one type of HA strat, but still dedicated).

Whereas selfhosting is hosting, though by oneself. The big difference is the level of dependence, how much one requires the stuff being up to the extent if it isn't that's an immediate blocker on other work. In the same way one would typically expect a commercial host to be more focused on uptime, redundancy and overall lack of surprises, selfhosting tends to be more conservative, throw more hardware at a problem, invest more time and effort in polish and smoothing interaction with the wider world, etc. Basically the stuff you'd expect for something where "if this goes down on Friday my weekend is shot" vs "if this goes down on Friday eh maybe I'll poke at it Sunday night or next week sometime".

Of course, one can also have both of these in the same home/SOHO/barn or whatever, just as businesses with decent IT will have some sort of minimal "lab" at least to do a bit of testing with before even getting to early staging. I myself am primarily on the selfhosting side of the spectrum at this point, but I do have a semi-isolated lab section as well where breaking world won't impact my work (nor result in upset family members!). No one right way to do it.

Edit: also on topic, no I don't have a dashboard :). I've at times considered products like Prometheus/Grafana/Heimdall and I guess now there's another one I could look at here, but I've never really been able to justify it vs other stuff. They're often fairly heavy or seem to have side effects to worry about (including security, I like to keep dashboards and IPMI highly isolated on VLANs or their own independent physical network entirely), and while it could be pretty and satisfying my stuff tends to either be working or it's glaringly obvious something is broken since I depend on it, or if it's an emergency condition it's blaring notifications at my phone anyway. And same as commercial service dashboards, to me it seems like to really be an addition a dashboard would need a fairly independent chain from what it's monitoring. Otherwise if the core goes down the dashboard also drops too. That means more dedicated hardware, even if only something like an RPi.

I could see a dashboard potentially being handy for unified monitoring of stats and softer errors, stuff that isn't an emergency itself but might be indicative of upcoming issues or issues with world (ISP always having problems at a certain time or failing to meet SLA say). But hasn't been truly compelling yet. Though sometimes the screenshots people put up make me quite tempted!

Edit 2: upon a bit more reflection, non-technical stakeholders are a factor as well. Just because something is selfhosted doesn't mean it's for oneself only, on the contrary selfhosters having stuff for friends/family, or a group of neighbors in an apartment/dorm having some shared resources is a common use case. A decent dashboard could serve the purpose of giving others a feel for what's going on. Both in terms of understanding/reporting issues without having to go to the admin(s)(you), but also just plain seeing more of what they heck you're up to. A lot of infra stuff in particular can take a certain investment of time and money but not look like much on the outside. Selling others can be valuable in and of itself, humans overall are visual creatures.