The video appears to be an edit of the two event videos into one. There's a firing of something at about the 20 second mark. After that finishes, at about 42 seconds, the recording changes to a slightly smaller view (slightly shorter lens on the video camera) and a clock appears at lower right. At 1:20, the main static firing appears to happen, which is significantly brighter and bigger than the one at 20 seconds.
The nose cone that will go on this set of tanks has been built and the reporting says the addition will be done there on the test pad. The nose cone has had its aerodynamic surfaces added.
I'm not sure if there will be another engine firing test once the nose cone is installed, but they are awaiting FAA approval to hop to approximately 50,000 feet. That event will be like nothing we've seen before.
SpaceX has developed a way for Starship to land that's mostly not like their Falcon 9 landings, and not like a Space Shuttle landing, which was a dead stick; that is, no thrust, no propulsion, but a slightly aerodynamic "lifting body." Starship comes in to the atmosphere belly first as a way to dissipate speed by lots of friction over lots of area. In the last several Starship lengths above ground, it suddenly fires engines and thrusters, goes through vertical, then lands on legs standing upright like the Falcon 9. This simulation video was up on YouTube by a group called C-bass Productions. I recall seeing a Twitter exchange while looking up something Elon had said. This video was there and he gave them a big thumb's up, then mentioned some detail that wasn't right. They fixed that detail and this is the improved version.
SpaceX lost a lot of Falcon 9 boosters before they finally refined things well enough to start landing them regularly. I'll probably faint if they nail the first landing instead of crashing the first try. Now it's easier to understand why they're currently building serial numbers 8 through 14. Along with Super Heavy booster SN1.