When using the saved object ui to export/import objects to move them between spaces I notice a few things we should fix,
When searching for a keyword with multiple results the export all button show the option to export only the filtered the results (in my example export 54/407 objects), but in fact, it exports all the objects Fixed in https://github.com/elastic/kibana/pull/44723

Selecting Export 54 objects exported all 407 objects instead of only the 54 objects in the results set
In addition, when using the bulk selection (which was the workaround due to the previous issue) it only selects to export the results showed in the first page (50 is the max), so users need to export every page separately.
Expected behavior:

When selecting the bulk checkbox it should select all objects in the results in all the pages
This is an interesting point; right now <EuiBasicTable /> only selects items one page at a time by default: https://elastic.github.io/eui/#/display/tables
IIRC there was a debate awhile back with @snide and @cchaos about how this case should be handled. Not sure if there has been any conclusion or further discussion since then.
Pretty sure I ran into the exact same issue here. Likely the same cluster ;-) https://github.com/elastic/kibana/issues/27250
Confusion is almost always solved by proper labeling of the buttons. We recommend to always put the counts into the buttons you use. Here's an example from the EUI docs.

From what I understand selecting all items was not possible from the component for technical reasons (persistance across pagination... or it could be thousands of items and the table doesn't have enough knowledge of the full data set...meaning you don't want individual items processed, you really want a bulk action that has little to do with the actual table guts).
Working around that...
Multiple ways to handle this from the design perspective if you want to retain an export all action, I'd suggest the following knowing that the table will only select the current page of items.
Change the button to a popover button if you want to retain both actions.
+1
Pinging @elastic/kibana-platform
A customer was bit by this today. Iterating on Dave's suggestion, here's a UX which I think will meet all of our requirements. Notice that there's only a single "Export" button in the screenshots below.
Per @snide's suggestion, this button should always be enabled and allow you to export all items. I think it's important to include both the count and the word "all" to indicate that, yes, you're getting everything, as well as the precise number as a sanity check in case you were expecting something different.

This one is obvious, but the ones you select are the ones that get exported. This behavior exists today. To @lukeelmers's point, you can only export from the table's current page. If you want to export more than that you'll have to do a combination of filtering and bulk exporting.
The button label makes it clear that you're exporting only what you've selected.

When a filter is applied, the button allows you to bulk export the filter result. This is what users currently expect but are unpleasantly surprised by when the UI doesn't deliver. The button label loses the word "all" to stand in contrast to the "export all" default state.

On a related note I noticed that the math doesn't always check out for the export modal. When we implement a solution we should be careful not to propagate this bug.

Pinging @elastic/kibana-app-arch
https://github.com/elastic/kibana/pull/44723 Fixes the filter export behaviour, but doesn't address the selection dissapearing between multiple pages bug.