Is this generally true for laptops / phones?

I've often wondered why I can tell by touch whether a device is charging or not from the slight "vibration" sensation I get when gently touching the case.

For ungrounded / 2-prong outlet devices, yeah.

It's often noticeable if you have a point contact of metal against your skin; sharp edge / screw / speaker grill, etc. Once you have decent coupling between your body and the laptop, you won't feel the tingle / zap.

They're called Y-caps if you want to delve deeper into them and their use in power supplies.

I get that too. I was wondering if it was just me.