Why does my tracking in InDesign appear wider than the exact same setting in Illustrator?

If you could repost your example of InDesign it would tell the story if you were showing both the paragraph styles AND character styles panel.

With InDesign, tracking is a setting that you precisely add or remove so-many-thousandths of em unit to the letter space width.

Not so with Justification letter spacing percentages of em width!

This latter does the same kind of work, especially in justified columns of text. But in this case, you are delegating a range of amount of tracking adjustment, trusting in the discretion of the InDesign typesetting engine to apply or not apply within a leeway as it sees fit.

Illustrator controls text first by character style, then paragraph style attributes.

InDesign is the opposite.

You should be using essentially only a paragraph style in InDesign.

Check on this:

Paragraph style is based on No Paragraph Style.

You don't also have a character style applied on the entire text. It should be on None in the Character Panel) when a whole paragraph is selected (where no individual words are italic nor bold, for example).

On the other hand, when you make a paragraph style in Illustrator, make sure what character style is under it. I avoid Illustrator's basic Normal Character Style, or at least edit it to have sensible attributes.

The justification and composer setting would also affect letter spacing:

Running through standard troubleshooting...the font is exact same and same size? Tracking is based on font size. Can you share screen grabs to illustrate?