If a picture of a screen is a screenshot, what is a video of a screen?

I'm looking for a catchy and nice-sounding word. A really nice sounding phrase would although be better than nothing.

I record my computer screen a lot and never really found a nice word to describe it like a screenshot. I also searched the web a lot and found nothing about it.

Example:

My mom: How do I get to the settings on my phone?
Me: I'll send you a _____(recording of my screen) so you can see how I get there.

"screen recording" is my favorite, but I am still not really satisfied. (UPDATE: I found a video of someone famous saying screen recording, I would appreciate if you comment with links to more videos like this with your favorite choices)... I also found about 100 videos on YouTube of people using this term, which I have not found for any of the alternatives mentioned in the question.

That said I did not find it on Lexico.com.

Here is a "screen recording" showing that "screenshot" is on Lexico.com, but "screen recording" is not.

Options I found unsatisfying:

screencast, screencap, videoshot, screenshots, screenmotionpicture, screenselfie, Screengif.

screencap is not common and confusing on top of that - here are some videos showing how this is used wrongly.

screencast is commonly used in certain fields (tech, design, photography, media and probably more). Here are a lot of videos showing this. My issue with this word is that it is very misleading and it will definitely confuse many people. @jmbpiano put this very nicely in a comment on the answer screencast :

This usage seems rather niche and if I were to first encounter it in another context, the suffix "-cast" would immediately evoke mental comparisons to "broadcast" and "webcast" (forms that are decidedly not static, playable on-demand video, but rather something that is being presented once at a specific time, possibly live and/or interactive).

Screencast

Similarly to many commenters here, I actually don't like this word much. Personally, I would probably use video capture. Individual tastes aside, however, screencast is a term that is very well attested in dictionaries, books, and software, and if you look at the evidence below, seems to be preferred overall.

Let's start with the

Dictionaries

Collins Dictionary (with thanks to Edwin Ashworth):

a digital recording of the display on a computer screen that may be viewed on another device

Macmillan:

a digital recording of computer screen output

Wiktionary:

a digital recording of a computer screen's display

Lexico:

noun A video recording or transmission of the data displayed on the screen of a computer or mobile device, typically with accompanying audio. ‘this tutorial contains a screencast demonstrating all of the steps’

verb (no object)
Record or transmit video of data displayed on the screen of a computer or mobile device, typically with accompanying audio.
                                               

On the other hand, screencast is not recorded in the OED, Merriam-Webster, American Heritage, or Cambridge.

Wikipedia

Here is the lede of the Wikipedia article "Screencast":

A screencast is a digital recording of computer screen output, also known as a video screen capture, often containing audio narration. The term screencast compares with the related term screenshot; whereas screenshot generates a single picture of a computer screen, a screencast is essentially a movie of the changes over time that a user sees on a computer screen, enhanced with audio narration.

True, in general, one should not take Wikipedia as a reputable source. However, my experience is that tech-related topics are usually treated quite authoritatively there, at least once the article has existed for a number of years (as this one has).

Use in published literature

Here are some books that use that terminology:

Screencasting for Libraries (source)
The Use of Screencasting in Higher Education: A Case Study (source)
iPad in Education For Dummies

Screencasting on desktops and laptops has been around for a number of years. Screencast software records whatever is displayed on your screen and enables you to add a voiceover narration during the recording. (source)

Sixth Grade Technology Curriculum: 32-lesson Comprehensive Curriculum

Have screencast and screenshot tools available as software, web-based tools, or add-ons. (source)

Use in software applications

Here are some examples of video capturing applications that use that term.

Kazam on Linux:

An example from Adobe:

Some other examples of software that uses this term: Jing, Screencast-o-matic, Bandicam…

Facebook uses the term screencast a lot in its pages for developers, i.e. here

Next, you upload a screencast of your app and how it is using the permission.

and here

You can use any of these accounts to test your app and create a screencast.
How can I test my app and record a screencast?
Provide a screencast.

and

Provide a Detailed Screencast and Clear Instructions = Quicker Evaluation

Our review team examines your screencast and follows your usage instructions to reproduce the personalization elements of each permission. Providing a detailed screencast and clear instructions will result in quicker evaluation of your submission.

(With thanks to Andrew Leach.)

I would call it a video screen capture. The Wikipedia article screencast says:

A screencast is a digital recording of computer screen output, also known as a video screen capture, often containing audio narration. The term screencast compares with the related term screenshot; whereas a screenshot generates a single picture of a computer screen, a screencast is essentially a movie of the changes over time that a user sees on a computer screen, enhanced with audio narration.

Wikipedia not withstanding, to me a screencast is more likely to be a live presentation than a recording, or at least one with a distributed audience, à la a broadcast. If you're just sending it to your mother, I wouldn't call it any kind of -cast.