Temurah, Chapter 7, Mishnah 2. This mishnah completes the topic we began in the previous mishnah: the four stringencies that apply to kodshei bedek habayis - items consecrated for the upkeep of the Beis HaMikdash - and do not apply to kodshei mizbeach, the items offered on the altar.
The first stringency - one who consecrates without specifying:
If a person consecrates something without specifying for what purpose he consecrated it, and says only "this is consecrated" - his consecration goes to kodshei bedek habayis and not to kodshei mizbeach. The main point here is that one might have thought that an unspecified consecration would be given to the kohanim as cherem, but that is not the case: when the one consecrating does not specify his intent, the consecration goes to bedek habayis - to the monetary value of the item for the upkeep of the Beis HaMikdash.
It seems that this includes even a case where a person consecrates an animal without specifying for what purpose, and it too goes to kodshei bedek habayis and not to an offering. This matter is the subject of a dispute in Maseches Shekalim (Chapter 4, Mishnah 7), and it appears that our mishnah follows the opinion of Rabbi Eliezer: although it is not proper to do so, and a person may not consecrate to bedek habayis animals that are fit to be brought on the altar, after the fact the consecration takes effect.
How would this look in practice? The person consecrated an animal, and since he did not say that it was for a particular offering, it is consecrated to bedek habayis. Afterward, the treasurers of bedek habayis will sell it to someone who needs an animal for an offering. The animal will ultimately be brought as an offering, while the money will go to the Beis HaMikdash for its expenses.
The second stringency - consecration takes effect on anything:
One may consecrate anything at all to bedek habayis. The Rash says: even wood and stones, and this is also the approach of the Bartenura. The Rambam focuses on the fact that consecration takes effect even on blemished animals or on animals of non-kosher species - these too can be consecrated, but of course only to bedek habayis and not for offerings. There is room to discuss why the Rash specifically chose wood and stones, since wood can indeed be brought up on the altar; and necessarily he means types of wood that are unfit for the altar, such as vine branches and the like.
The third stringency - me'ilah applies to what grows from them:
There is a prohibition of me'ilah with regard to produce that grows from items consecrated to bedek habayis, which is not the case with kodshei mizbeach. For example, a person consecrated his hen to bedek habayis and the hen laid an egg: just as one who eats the hen transgresses the prohibition of me'ilah - since he derives benefit from something consecrated to hekdesh, and he must bring a special offering called an asham me'ilos, pay the value of the hen and add a chomesh, a fifth of the value (twenty-five percent), as an additional penalty - so too with regard to the egg. At the time of consecration there was as yet no egg, and nevertheless, if it was laid afterward and someone came and ate it, he too has committed me'ilah, and those same consequences apply to him.
The reason for this: the hen was given to the Beis HaMikdash as a financial resource for its upkeep, and therefore the egg that it lays is included in the gift as well. The technical term is that the entire gift - the hen and its eggs together - falls under the category of 'kodshei Hashem', items consecrated to Hashem, meaning to His Sanctuary and its upkeep.
By contrast, if one consecrates a goat as a shelamim offering - the milk of that goat is not included in kodshei Hashem, since it does not go up on the altar but is a separate item. Therefore, one who rides on the goat and derives monetary benefit from it has certainly transgressed the prohibition of me'ilah and is liable to bring an asham me'ilos; but one who drinks the milk of a goat consecrated for the altar, although this is forbidden to derive benefit from, has not technically committed me'ilah, since the milk is not kodshei Hashem and does not go up on the altar. The same applies to one who eats the egg of a turtledove that was consecrated as a bird olah: it is forbidden to derive benefit from it, but there is no prohibition of me'ilah and there is no need to bring an asham me'ilos.
This, then, is the difference: with kodshei bedek habayis there is me'ilah even with what grows from them - with the milk and the eggs; whereas with kodshei mizbeach the milk and the eggs are not subject to the technical prohibition of me'ilah.
The fourth stringency - "v'ein bahem hana'ah l'kohanim" - "and the kohanim derive no benefit from them":
The kohanim have no benefit from items consecrated for the upkeep of the Temple. When a person consecrates money or objects for the maintenance of the Beis HaMikdash, everything goes to the Temple itself, and the kohanim have no share in it, nor does anyone else who serves in the Temple. In contrast, when one consecrates something for the altar, there is generally a portion of the offering that goes to the kohanim: most offerings are eaten by the kohanim, at least in part, and even in the case of the olah, which is burned entirely, the hide is given to the kohanim. It emerges that the kohanim do derive benefit from items consecrated for the altar, unlike items consecrated for the upkeep of the Temple, in which they have no share whatsoever.
It is worth noting that there are indeed certain offerings consecrated for the altar in which the kohanim have no share, such as the bulls and goats that are burned completely, as on Yom Kippur, and likewise the meal offering of a kohen, in which he has no share. So there are examples of items consecrated for the altar that provide no benefit to the kohanim. But in general terms, the point is that with items consecrated for the altar there can be benefit for the kohanim, whereas with items consecrated for the upkeep of the Temple, the entire consecrated item is holy, and no part of it is designated for the benefit of kohanim.
To summarize: there are four stringencies that apply to items consecrated for the upkeep of the Temple and not to items consecrated for the altar - one who consecrates without specifying has consecrated for the upkeep of the Temple; the consecration takes effect on anything at all, even on wood and stones and on animals that are blemished or of a non-kosher species; the laws of me'ilah apply even to what they produce, to milk and to eggs; and the kohanim derive no benefit from them at all.