Segments
Some objects are naturally segmented, they have marks or narrowings between segments. These are places where the object can be easily and naturally separated. The segments are usually all alike in form. Think of an orange.
Parts
Some objects are compound objects that consist of an assembly of smaller dissimilar objects. We can separate these compound objects these into their constituent parts. Think of an internal combustion engine.
Pieces
Some objects don't have obvious segments but can still be divided into pieces at arbitrary points. The pieces need not be even in size and there is an undertone of destructive or irreversible breaking. Think of a (stereotypical circular uniform) cake.
Fragments
Some objects, when subjected to some sufficiently violent force, can shatter into multiple fragments of mostly random size and shape. If the other fragments are lost, you may find only one fragment and have no other knowledge of the form of the whole object. Think of a dropped Ming vase.
Sections
Some objects are designed to be cut apart or are commonly cut apart. The word section is derived from the Latin word for cutting and may be appropriate for a deliberate and careful cutting of some extract from a larger source. There is, to me, an implication that the cutting points are not accidental. Think of plumbing pipes
English text
Written English language text is usually written in sentences, paragraphs and perhaps chapters. These form obvious segmentation points, so when your extract is made at a balanced pair of such boundaries, the term segment is more appropriate. However, why not just use sentence or paragraph as appropriate?
If you spilled ink onto a page of text, it might be better to say that a part of the text was obscured - since (unless by unlikely coincidence) the obscured part is not an exact sentence or paragraph.
If a page of text is burnt or torn and scattered, you might consider any remainder to be a fragment.
As HorusKul commented, since successive English sentences are not often very similar, they are not very much like segments and the word section is more likely to be appropriate.
Updated to clarify segments, pieces, parts and sections. Updated: fragments.
A "photo" is something that was taken with a camera.
Short for "Photograph". Photo means 'light'.
An "image" is something generated or a representation of something in any other way. This can be a combination of different photos, part of a photo that has been greatly edited, or really, anything that has been made in Adobe Photoshop.
All elephants are gray things, but not all grey things are elephants.
All photos are images, but not all images are photos.
Best Answer
Single definitions cause most of the trouble here, though that’s made more confusing by the idea that "Section" is smaller than "Part” which has little and usually irrelevant justification , don’t you think?
“The front section of the car contains the headlights” might be true but it would not be more correct than “The front part of the car contains the headlights”, would it?
However, “a headlight is part of a car” would be correct while “a headlight is a section of a car” would be fairly clearly wrong, because of vocabulary, not grammar. Does anyone really think that has as much to do with custom or practice or idiom as with strict definition?
Section and Part can be generically similar; even interchangeable, but each has more than one meaning and some are by no means equivalent.
Yes "in sections of Canada, French is the first language" is correct in exactly the same way as “in parts of Canada…” Personal preference more than anything else may make either more desirable.
A Lego spaceship is indeed made of Lego parts, not Lego sections and “section” does describe areas not normally discretely divisible, but that is like sections of a building only in terms of technical drawing; just possibly of architecture but not in terms of the act of construction.
Generically the front Part of a spaceship or building or car might just as well be the front Section but specifically the Parts of a car include axles, wheels and nuts and bolts each in and of itself complete but also, individually, largely useless.
That is quite different from the from the way in which the front - or rear - Part of car includes all of the above. Specifically, a wheel is a Part but never a Section of anything. In a rather different context, Section has much more specific meanings which are wholly different from Part.
Etymologically, Section can be either noun or verb and either way, comes from Latin Sectio, to cut - more obviously seen in Dissection, for instance.
It’s very easy, mentally, to separate or “cut” front from back or left from right and only a little skill is required to do that with a laboratory sample, or to a patient in an operating theatre but on a building site or in an aeroplane factory, that might be impossible.
Between the two meanings lies the Section used in technical drawing. It’s easy both to imagine and to physically see the front or rear or left or right or top or bottom of whatever is being built but in most cases it’s difficult and many times it’s impossible to actually see how a car or a building or a plane would look arbitrarily cut it in half three feet from the back or specifically at the point where the axle meets the chassis or where the joists sit on the wall.
Very vaguely similarly an orange can be viewed as a whole object. Parts of the orange include the skin, the pith, the pips or seeds and the fruity segments. The orange can be cut or Sectioned any way the chef or diner prefers but Parting an orange would not be a realistic concept.
The fruity segments of an orange could be Parted from the skin, but not by slicing or Sectioning.
Segments of an orange can be Parted but not Sectioned from the rest, or from each other.
The front Section of any object is a purely arbitrary conception in which Section could as easily be Part.
The verb To Section, as in a bodily organ or a laboratory specimen, is a physical act highly unlikely ever to be compared with To Part even though pedantically, the Parting of the waters of the Red Sea might be thought of as “Sectioning”. To Section is to slice or cut a single thing into pieces, probably damaging if not destroying both the thing and the resultant pieces; to Part is to separate or disconnect the individual pieces of a complex whole, always n such a way that they can be reassembled to re-form the original item.
A “Section through A” in technical drawing is a purely imaginary construct having plenty of use to architects or builders or designers or engineers or technicians but no real meaning in physical terms. In terms of technical drawing, “a Part view through Section A” would be tautological, at best. Section A 𝘪𝘴 the Part view; it cannot be viewed through itself.
Broadly, a Part is a thing physically complete, even though probably useless, in and of itself; designed to be combined with other Parts of a whole which by definition, is greater than the sum of those Parts.
Either a Part or a Section might generically be a portion or area or region of something else but in such a case the shape, size and position would be arbitrarily defined.
Contrarily a Section can specifically mean either a portion - generically but never specifically, a Part - sliced off or out of or through a larger object, or a view of the remainder after an object has been sliced into pieces, either physically or imaginatively.