Taharos, Chapter 2, Mishnah 6. This chapter maps out the degrees of tumah, tracking exactly how far tumah can travel once it enters food, and how the answer changes depending on whether we are dealing with chullin, with terumah, or with kodesh. Our mishnah takes two specific cases: food of chullin that has reached the second degree, and food of terumah that has reached the third degree.
Before the mishnah itself, one principle has to be in place, and it comes from outside our maseches. In maseches Parah, chapter eight, mishnah zayin, we are taught:
"Kol haposel es haterumah metamei es hamashkin lihyos techilah"
Anything whose contact with terumah is strong enough to disqualify it renders liquids tamei as a techilah, that is, as a rishon. This is the great exception in the whole system. Ordinarily every contact steps the tumah down one level: a rishon produces a sheni, a sheni produces a shelishi. Liquids do not step down; they jump up. A sheni that touches liquid does not leave behind a shelishi, it leaves behind a full-strength techilah, and that liquid can then go on and render something else a sheni. The upgrade is a rabbinic enactment, yet once it applies we treat the liquid as a genuine rishon in every practical respect.
Now to the mishnah's own words. It begins with chullin: "Hasheni shebechullin", food of chullin that carries second-degree tumah, and it lists two consequences. Where such food comes into contact with chullin liquid, the mishnah says it is "metamei mashkeh chullin": the liquid acquires first-degree tumah, precisely along the lines of the ruling cited from Parah. Where it comes into contact with solid terumah, the mishnah says "ufosel ochlei terumah": the terumah slips to third degree, which leaves it unfit for use, though it no longer holds any capacity to hand tumah on to a further item.
The mishnah turns next to terumah: "Hashlishi shebaterumah." Within the world of terumah, third degree is the last rung; such food can no longer render other terumah tamei at all. Kodesh, however, is held to a finer standard, so this shelishi still has an effect there. Regarding liquid, the mishnah says it is "metamei mashkeh kodesh", the liquid of kodesh it touches becomes tamei. Regarding solids, it says "ufosel ochlei kodesh", the kodesh food it touches is rendered unfit, meaning that the food itself is tamei yet possesses no strength to convey tumah any further.
To that the mishnah attaches a condition: "shena'asu letaharas kodesh," all of this holds where the terumah in question was handled and prepared under the stricter standards of the taharah of kodesh. It is precisely because it was guarded at that level that it retains the ability to affect kodesh in this measured way. The Bartenura notes that this point is the subject of a dispute.
"Aval im na'asu letaharas terumah": should the terumah have been kept only to the ordinary standard of terumah taharah, without the added stringencies of kodesh, its status vis-a-vis kodesh becomes considerably harsher. It now functions as a techilah, and the sequence unfolds from there: whatever it touches becomes a sheni, and whatever that touches becomes a shelishi. Those are the two items the mishnah has in mind when it says the terumah "metamei shenayim", it makes two things tamei with real transmitting force. The fourth item in the chain, a revi'i in kodesh, is covered by the words "ufosel echad bakodesh", it is merely disqualified. The choice of terms here is exact: once an item is tamei but can no longer convey tumah onward, the mishnah pointedly avoids metamei and uses posel instead.
So our mishnah gives us two snapshots of the same system: chullin at the second degree still reaching liquids and terumah, and terumah at the third degree still reaching kodesh, with the extent of that reach determined by the standard of taharah under which the terumah was originally prepared.