die Leinwand
screen
The large white surface in a cinema onto which films are projected.
Der Film kommt nächste Woche auf die große Leinwand.
The film comes to the big screen next week.

screen / canvas
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screen
The large white surface in a cinema onto which films are projected.
Der Film kommt nächste Woche auf die große Leinwand.
The film comes to the big screen next week.

'Leinwand' consists of 'Lein' (linen, a fabric made from the flax plant) and 'Wand' (wall). Originally, then, it was a 'wall made of linen fabric.' This origin explains the different meanings, all of which have to do with a kind of fabric surface.
Früher wurden Segel für Schiffe aus robuster Leinwand gefertigt.
In the past, sails for ships were made from robust canvas.
The meaning of 'Leinwand' (screen/canvas) is usually clear from the context. Words like 'Kino' (cinema) or 'Film' (film/movie) point to the projection screen, 'Maler' (painter) or 'Farbe' (paint/color) to the painting surface, and 'Stoff' (fabric) or 'Zelt' (tent) to the material.
Der Künstler spannte eine neue Leinwand auf seinen Rahmen.
The artist stretched a new canvas onto his frame.
In a cinema context, 'Leinwand' (screen) is almost always used with the preposition 'auf' (on). Fixed expressions are 'ein Film kommt auf die Leinwand' (a film comes to the screen / is released) or 'einen Star auf der Leinwand sehen' (to see a star on the screen).
Viele Fans freuen sich darauf, ihren Lieblingsschauspieler wieder auf der Leinwand zu sehen.
Many fans are looking forward to seeing their favorite actor on the screen again.
screen
'der Bildschirm' and 'die Leinwand' can both be surfaces on which you see images. The important difference is the technology: a 'Bildschirm' belongs to an electronic device and lights up itself, for example on a computer, television, or mobile phone. A 'Leinwand' is a surface onto which an image is projected, such as in a cinema, or a fabric used for a painting. The words can be confused because both have to do with films or images. For devices, you say 'Bildschirm'; for the cinema, a projector, or painting, you say 'Leinwand'.

Im Kino war die Leinwand so groß, dass alle den Film gut sehen konnten.
In the cinema, the screen was so big that everyone could see the film well.
Nach zwei Stunden am Bildschirm tun mir die Augen weh.
After two hours at the screen, my eyes hurt.