Trying to give some insights, just getting in details what Andrey already said.
Difference between visits and TC instances
If you break down both metrics by the tracking code just like above, the "TC instances" shows how many times the tracking code has been set (is on a single server call). in most cases the user arrives on your website with the tracking code, thus counting for visit and "TC instances" (both get 1)
but assume the user is coming back to your website later (new visit) without setting a new tracking code. that means, the "old" tracking code is still valid (if not already expired) and the tracking code gets a new "visit" (without a count for "TC instances"). or in other words: as long as the same user arrives on your page without a new tracking code (and before the TC expires), it will count as a visit in your table
Why last touch "natural search" on breakdown?
basically as written above, the user arrived (after the initial visit) on your website without tracking code.
it doesn't matter if it is in the same visit or later, as long as the tracking code has not expired.
remark: you see a difference on the "tracking code visits" (sum -> 1'479) lower than single rows (977 + 686). the difference are those match "same visit" because the sum is de-dublicated (1 visit for the tracking code) both both a 1 for each row.