Is 's' in Physics Notation Referring to Arc Length or Speed?

[mill]

Equation 1

$\frac {d\vec T} {ds}$

2.
s=arc length=∫|v|dt

3.
|v|=speed

4.
ds/dt = |v|

(distance/time)Does the s from the notation of arc length or the notation of speed? derivative of arc length vs derivative of speed

I am getting confused because ds was referred to as distance in a video I watched, and I thought the s stood for the derivative of the arc length, but speed (s) is also being used around the textbook.

 

[saminator910]

the $s(t)$ is notation for the distance traveled, therefore, the change in distance with respect to time is the speed, as opposed to the velocity, which is displacement over time.