How to provide embeddable dynamic code snippet for other website to provide my data/visualization?

I want to ask a question which I think I am not able to formulate enough clearly :(

My target is to provide a way, maybe some code snippet:

• which can be embedded by other websites;
• after embedding our code snippet, a small area will be shown on their websites, as a widget;
• this widget retrieves data from my service, which is a RestAPI web service, and shows the visualisation in the widget;
• the data retrieval is dynamic, or periodic, let me say, every hour, and after getting the new data, the visualization will be refreshed;

In my opinion, this is very similar to many portal websites like yahoo, or FAZ.net in Germany, which has some weather widgets or stock widgets on their websites. The data provider for these web widgets is somebody else. And the web widgets fetch and visualise data by themselves. Yahoo or FAZ.net don't need to worry about other things, they only need to embed these web widgets.

This is basically I want.

I cannot formulate my question well, because, first of all, I don't know if there is an dedicated terminology/standard/protocol for this kind of technique?

And second, I understand, nowadays most websites are built using different CMS or website builders using different programming languages, they all have their own skeleton, definitions etc. Is it easy to realise what I want easily with these different web frameworks/programming languages?

I will be very appreciated for your help!

Many thanks in advanced.

Best regards
Tek