Likely two separate cars. The first one has a signature emblem that I don't see on the second. You could custom order any color that Lotus had available. I'm told there was one "purple" Roadster here in Austin; this may be "purple."
No, I think it is the same car.
The emblem is for "Sport" (not Signature.)
It is an early 2010 Roadster Sport 2.0, but has been updated along the way to have newer parts including 2.5 bodywork, backup camera, etc.
I think it was first painted a copper color, then repainted in a (nearly) unique "Candy Apple Red" AKA "Twilight Red" that was custom. I say "nearly" because Toyota CEO liked it so much that a 2nd (right hand drive) was done in that custom color to give to him as a gift. I don't think it is a "standard" Lotus color.
Toyota president Akio Toyoda gets free Tesla Roadster at Tokyo store opening
( The USA one in the videos still has the 2.0 black forged wheels, not the newer 2.5 "pinwheels". )
By the way, that "purple" Roadster you mentioned was a Lotus "Aubergine" paint, maybe one of a kind, sold to someone in Hollywood, CA recently.
Very different color...
( Built approx 58 cars after the "Candy Apple Red" one...)
Here is another old pic of the one I think is in the video (before it had sport badges affixed, and what I think is that same one that got 2.5 bodywork later.)
I think the color is similar to the "Signature Red" they offered on the first batch of Model S production.
(They end up looking slightly magenta under some lighting.)