Here is the facts:
SPEED: This is what is called a 'scalar' quantity! Speed is the rate at which you travel a certain 'distance'.
VELOCITY: Velocity is what is called a vector quantity! Velocity is the rate at which you travel a certain 'displacement'.
First an example to clear up these two!
Say I am racing around a 100m race track and it takes me 10s to complete 1 lap!
My distance travelled of course is 100m, BUT my displacement is 0m. According to my displacement I've gone nowhere.
Thus;
distance 100
speed = ------------ = ----- = 10m/s
time 10
displacement 0
velocity = ------------------- = --- = 0m/s
time 10
Now, delta-v (Δv)
ΔV - This is also called 'change in speed'. Say I'm travelling at 10m/s (u), then, I decide to travel a bit faster to, say, 50m/s (v). Then my Δv is;
Δv = v - u
Δv = 50 - 10
= 40m/s
Therefore I can say my change in speed is 40m/s.
Does this help!