Haha, yes, it does hurt like fuck.
In less than a second of exposure, it was enough to make the skin on my finger tip start to blister. It was a small blister, and disappeared within a couple minutes, but after about 2 seconds you could see that the upper layer of skin had separated and become white, which is the indication of the beginning of a blister (Not the first time I've been blistered by burns)
Tesla coil shocks are much the same as what you described. There was actually less vibration and more of a tingle in my case, but otherwise it's pretty much the same. Of course, it didn't cause any muscle pain or anything.
However, AC house current shocks are a different beast entirely. I could feel my arm pulsing with the current, and my hand was stuck clenching the side of the socket. I was crouched down, so on instinct, I fell backwards and my hand came off the socket, but it scared the crap out of me, because I wasn't expecting it. The first time I did that it was my own fault for not being careful (We were painting, a socket was sticking out of the wall, and I was paining near it, and wanted to move it, but I just happened to grab the screws on either side), but the second time wasn't (We were working in the basement of the place we were fixing up, the power had been off there earlier, and the lights were all off, I was fixing some of the wall socket wiring and stuff, and grabbed one, only to find out someone had turned the fucking power on.)
They are scary shit, because you know exactly what's happening right away. It's not something that ou can kinda go "hmm, what's this?" It's more like "Oh fuck, I'm being electrocuted!"