EDIT: This question didn't help me.
Should I say:
This is the point where the road begins
or
This is the point where the road starts
What about the arc endpoints instead? Should I say:
This rope connects arc's start point and arc's end point
or
This rope connects arc's beginning point and arc's end point
To my taste, begin works better with roads and start works better with arcs. Is it correct? Is there a reason for it?
The two words 'begin' and 'start' are very close logically, 'something has been caused to happen', so their primary differences are collocations and connotations.
'Begin' sounds more formal and attaches to more abstract things.
'Start' is more informal and is more likely about concrete processes.
A teacher might say "Let's begin the lesson." and the student "We started studying.".
Etymologically, 'begin' is classic Germanic, a common cognate in all Germanic languages. 'start', while also Germanic, was more about a movement: leap, tumble, or fall, which in ME was to flinch ('startle') and by semantic drift 'to set in motion' by Early Modern English. I mention this because usually a formal/informal word pair in English has a French/German source. But whatever the history, most of the older versions of 'start' are obsolete and is currently mostly the same as 'begin', modulo register.
As to your particular words, I don't find any preference for start or begin with road or string themselves. It is purely the context which might give a very subtle nudge for start or begin.
