Right - - in an effort to dispel any suggestion that my comments are 'Half-truths' I've created drawings of the 'Screw-cutting' process.
First, the most important dimension of any thread is the 'Effective Diameter', the OD and Root are both secondary - as long as they are not wildly beyond the 'norm'. ie. if the OD is truncated, the thread will generally still be OK -
as long as the Effective Dia. is within tolerance.
It should be borne in mind that Screw-Cutting is one of the most demanding operations in lathe work and there are two major methods by which threads can be 'Screw-cut' - the least demanding is by setting the top-slide over at half the thread form included angle (30° for Metric, 27½° for Whit. etc.).
!!!!! - the 'Editor' now precludes the inserting of 'special characters' using the [Alt] keypad !!!!! I had to resort to "copy'n'paste" to get '°' Grrrrrrrrr.........!
The more demanding is feeding the tool in perpendicular to the work - this causes material to be removed from both side of the thread causing a conflict with the swarf folding in on itself.
However, life is a compromise and if you wish to use a threading Tip (or single point tool), which is designed to cut (say) a 1mm pitch but the thread being made is 1.5mm pitch then the second option would allow you to make the lateral adjustment to maintain the root flat width without having to feed too deep.
Pictures speak much louder than words, so :
This shows a single point tool (or 'Partial Profile' Tip) (Blue) being used with the top-slide at the half-angle. Feeding deep enough to maintain the correct Effective Dia. takes the depth into the Magenta region. If you were to stop at the correct depth of thread (the shading pink area) you would then have to make a 'lateral adjustment' to remove the 'grey' area but with the top-slide at the half angle and the need to maintain the 'saddle' in correct mesh ( with the lead-screw) that becomes quite difficult.
If you take the compromise (Green), with the top-slide at zero deg., then lateral adjustment is possible.
The drawing shows an extreme example where the tip used is very much smaller than would normally be considered - just to make the example more obvious.
If you now consider a thread form which has a rounded crest & root (such as Whitworth), I'm sure you will appreciate that there are many more difficulties :
Here, again, using a Partial profile or single point, without 'truncating' the OD (pale blue section) you can see that the green section would interfere with the internal mating thread. To create a thread with the correct Effective dia. the cut depth would have to extend into the magenta section. Lateral adjustment is even more complex to figure out in this case (though not impossible).
I do accept that for many applications threads can be successfully produced with both single point tooling and partial profile tips but if you are 'Screw-Cutting' it is usually because you are dealing with 'Special' threads (outside the Standard OD/Pitch combinations) or you want the best possible thread under your absolute control.