What is the difference between uniform velocity and constant velocity? I think that uniform velocity implies constant speed but not constant direction. while constant velocity implies constant speed without any changes in direction.
Both tell us that there's no acceleration (since magnitude of velocity is constant).
The same goes for acceleration: both imply constant magnitude, but only constant acceleration means that there's no change in its direction.
However, a lot of people on the Internet argue that whether it's the other way around or that there's no difference at all. Who's right and who's wrong?
 A: I don't believe the distinction between "uniform" and "constant" in this context is important: I would use them interchangeably. I certainly have not encountered any serious technical usage of these terms in this context that relied on an implicit knowledge of any such difference. In general, I would take both "uniform velocity" and "constant velocity" to mean a velocity vector that is not changing in magnitude or direction. The same goes for acceleration. If this is not the case in a certain situation and the difference between "constant velocity" and "constant speed" is important, you can expect the meaning to be clear from the context, or stated explicitly.
As for your third sentence, a constant magnitude of velocity does not mean there is no acceleration. Any body rotating in a circle at constant speed has a non-zero (centripetal) acceleration.
A: Regardless of what you call it, in order for an object to not be accelerating both the magnitude of its velocity (speed) has to be constant AND its direction (path) needs to be in a straight line (aka rectilinear motion).
In order for the direction of an object to change it must experience a net force and thus an acceleration.
Take the simple case of an object moving in a circular path at constant speed. It experiences a centripetal acceleration of magnitude 
$$a=\frac {v^2}{r}$$
And a force of 
$$F=m\frac {v^2}{r}$$
Hope this helps 
A: The word uniform means the "same in all cases". Therefore, constant and uniform are often used interchangeably. Just be careful about where and when the sentence is used. For instance, if I say a car is accelerating uniformly in the xx-direction, then it has a constant acceleration in that direction.
In the case of a car moving around a circle with a constant speed, then we have uniform circular motion, but the velocity in this case is not uniform, it is changing direction. The word "uniform" in this case means it is travelling at a constant speed, and in such a case the magnitude of velocity is constant, but the direction changes.
Then, constant is with respect to time domain and uniform is said to be with respect to the space domain.
Now, consider a metallic cube. Now we say that mass is uniform if the mass per unit volume is same everywhere.
Then, what is constant?
Consider the same example. Now we say that the mass is constant if the mass of the whole cube does not change with respect to time.
P.S.: I went through J. Redman's answer and interpreted it in a lucid way. That is why the first two paragraphs of this answer resemble J. Redman's answer.
A: Constant and uniform velocity mean the same thing, which is covering equal distances in equal intervals of time WITHOUT changing direction. Direction cannot be changed as velocity is a vector.
