die Spitze
tip
The pointed, narrow end of an object.
Die Spitze des Bleistifts ist abgebrochen.
The tip of the pencil has broken off.

tip / top / lace
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tip
The pointed, narrow end of an object.
Die Spitze des Bleistifts ist abgebrochen.
The tip of the pencil has broken off.

The noun 'die Spitze' (tip/top/lace) derives from the adjective 'spitz'. If you know that 'spitz' means 'sharp' or 'pointed', you can more easily understand most meanings of 'Spitze'.
Vorsicht, die Nadel ist sehr spitz!
Careful, the needle is very sharp!
For the meaning 'Führungsposition' (leadership position), the preposition 'an' is used. 'An der Spitze sein/stehen' describes the position, while 'an die Spitze kommen/gelangen' describes the movement to get there.
Sie steht seit fünf Jahren an der Spitze der Organisation.
She has been at the head of the organization for five years.
To say what something is the tip of, the genitive or the preposition 'von' is often used. This is very typical for the literal meaning.
Die Spitze des Eisbergs ist nur ein kleiner Teil des Ganzen.
The tip of the iceberg is only a small part of the whole.
The expression 'eine Spitze gegen jemanden' means a small critical or ironic remark. It is often combined with verbs like 'sich erlauben' (to allow oneself) or 'sich nicht verkneifen können' (to be unable to resist).
In seiner Rede erlaubte er sich eine kleine Spitze gegen die Opposition.
In his speech, he allowed himself a little dig at the opposition.
When 'Spitze' appears in the context of clothing, fabrics, or decoration, it always means the fine fabric. Typical verbs are 'verzieren' (to decorate) or 'einnähen' (to sew in).
Ihre Bluse hat einen Kragen aus feiner Spitze.
Her blouse has a collar made of fine lace.
end
'das Ende' and 'die Spitze' can both refer to an outer point of something. 'das Ende' is general and means the last or outermost point, for example of a road, a rope, or an object. 'die Spitze' means a particular kind of end: it is often narrow, pointed, or at the very top, for example on a pencil or a mountain. Learners may confuse the words because a 'Spitze' can also be an end. But not every 'Ende' is a 'Spitze'. When the shape or height is important, 'Spitze' fits better.

Die Spitze des Bleistifts ist abgebrochen.
The tip of the pencil has broken off.
Sie hat das Ende des Seils an der Tür festgebunden.
She tied the end of the rope to the door.