Since you brought it up, at about 8:14, what kind of guitar is Prince playing?

https://www.youtube.com/watch?v=LNrAFb3I2js" rel="nofollow - https://www.youtube.com/watch?v=LNrAFb3I2js

https://www.youtube.com/watch?v=WniSt0yhroE" rel="nofollow - https://www.youtube.com/watch?v=WniSt0yhroE

That's a 4-string electric bass.  It has a 'wierd' shape, and it's being fed through a guitar effects proccessor set up with an ADSR envelope filter (like an automatic 'wah' pedal) but aside from that, it's no different from any other 4-stringer.  The tuning machines are located in the tailstock (to his right side) rather than in the headstock, which is no different from my Steinberger Spirit-5.

Look here-  3rd and 5th photos down:

http://www.identitycrisisqca.com/photos.htm

Junior Brown plays a 'Guit-Steel', it's basically two instruments bound together in one body-  the upper is an electric guitar, the lower is an 8-string (non-pedal) steel guitar. 

The guitar portion is a bolt-on neck of the typical Telecaster shape and length, the body contains three pickups similar to a telecaster or stratocaster form-factor, but they're slightly wider than a typical Fender form-factor, and he has the neck position pickup angle reversed, with a bridge position, and the third is offset closer to the bridge, than neck, so his tones are neither Telecaster, nor Stratocaster in their timbre.  When I saw him last, I believe the pickups were EMGs (predecessor to the FT series), but couldn't tell for certain, because the surfaces were well worn (he's like me- shows no mercy towards instruments).  The bridge on his guitar portion is actually an aftermarket (non Fender) fulcrum-type tremolo, but it's for a LEFT_HAND guitar- the tremolo arm would normally thread in on the bottom, he's got it on top.  He doesn't run with a tremolo arm in the guitar, instead, he hooks his fingers under the back of the tremolo, and just pulls it up and forward to drive the strings down.

The Steel is an 8-string, and it  appears to be a fairly typical setup. He's got a stand that, when onstage, his instrument rests on it.  He can stand and walk around while playing the guit, but to switch to steel, he sets it on the stand and flattens it out, to reach over and slide.

He is an extremely talented, and very funny man.

BTW... in the 1995 Music City video-  the gal playing the acoustic-  that's Junior's Wife, Tanya Rae- she's not only a musician, she's a co-writer, and the band/business manager. 

Yeah, there's nothing special about the instrument.  I've got a Line6 PODPro in my home studio rack that has several patches like that... but as silly as it seems, I never use any of that stuff.  I set it up for the amp/room sound that I want, and play it for the recording.

When I play live, it comes out of the instrument, into a DI box, to the mixer, and also to my stage (monitor) amp.  If you look close at that Steinberger, you'll notice that it only has a neck-position pickup, and no volume or tone knobs-  the pickup is wired straight to the jack.  If there's a weird sound coming out, it's my fingers doin' it, not some pile of electronics.