This issue involves 3 different aspects.

Time-splitting method in the UI
Time-splitting method is not a nice name, it is not even nice to type. It sounds like something very complex and weird and it does not even reflect what it really is as not all time-splitting methods split the duration of an analysable element in parts.

To update all the internal references to time-splitting method would be hell, but we can change the references in the UI by something more user-friendly. After asking for suggestions emdalton1 proposed "Prediction interval" or "Analysis interval". I personally like "analysis interval" because those same intervals are also used to generate training data.

The name of the time-splitting methods in core
Naming specific time-splitting methods has also been challenging because:

1. We talk about "the start" or about "the end" without mentioning the start or the end of what. The name of the target helps here, but still, it is not 100% clear. This is the price for having reusable elements in this API...
2. We need to inform users of too many things in just 1 line
   1. How many predictions (i.e. intervals for analysis) will be generated?
   2. When will the system generate predictions?
   3. What interval will be used during each of the analysis?

Therefore, as part of this change we should also review the names we have been using to describe the time-splitting methods we have in core as these options would not directly make sense when put next to a field named "Analysis interval". I propose to use the help link to clearly explain #1, #2.1, #2.2 and #2.3.

I am writing a proposal for this that will be also useful for MDL-65633. This is the draft image.

The "Get predictions" action is not a get predictions on-demand
I can imagine someone that does not know much about this system expecting a model to generate predictions every time a user clicks on "Get predictions". This is not how time-splitting methods work and it is related with the point #2.2 in The name of the time-splitting methods in core. A model that uses a time-splitting method that only generates 1 prediction for each sample will calculate the indicators and generate the prediction the first time the "Get prediction" action is executed. The second time it is executed we will detect that this model already generated a prediction for that sample and will return a No new predictions yet message. The same happens with time-splitting methods that generate predictions after each quarter of the course. After the first quarter of the course a prediction will be generated when "Get predictions" is executed or when the cron executes it automatically. If a site manager manually executes "Get predictions" the following day, the No new predictions yet message will be displayed again and no new predictions will be generated until the next quarter of the course is over. We either need to rename the Get predictions action or to reword the No new predictions yet message.