Beyer speed figures are heavily, almost exclusively, based on time, with coefficients for how the track is playing etc. In other words time is the yardstick that horses are being measured by, with the aforementioned adjustments.
TimeformUS figures take into account the time, but also the pace and shape of the race and other factors like weight carried etc.
Traditional Timeform figures in GB/IRE were basically handicap ratings, based on heavily on a visual performance and how one horses stacks up against another. So the yardstick is more the horses themselves. So horse A wins a race by 7 lengths, getting 3 pounds from B on good ground going 10f, and horse B is rated at 105lbs (number pulled out of the air), then they give horse A a rating of let’s say 109. Then next time out horse A loses to horse C by half a length at level weights, then we can say horse C is 111 lbs etc.