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.
You have compared tracking code with the marketing channel dimension. They are possible reasons why last touch natural search is showing for cid, like both tracking code and marketing channel have different expiration.
Marketing channels have a rolling 30-day expiration, whether a channel was touched or not. Tracking codes have an expiration based on when the variable was defined.
You may want to check the Paid Search detection rules in the report suite configuration to make sure that the traffic coming with "_ppc_" in the URL from search engines is detected as paid search.
Could you also clarify what metric is used in the freeform table above? - set it to tracking code instances to check whether the Natural Search bucket will still be shown under that tracking code value.