How can you set two eruvin? It's making your residence in two places!

Question

The introduction of ר׳ פנחס קהתי's to מסכת ערובין reads, in part (in my own translation and with emphasis supplied):

… that residents of the courtyard not carry from their houses to the courtyard or from the courtyard to their houses unless they made an "eruv [chatzeros]", i.e. that all the residents place food before the sabbath in the house of one of their number. By doing so their domain becomes combined, they themselves are as if they're all concentrated in the residence in which the eruv food is placed, and the entire courtyard with its houses becomes as if one homogeneous domain.…

… makes an "eruv t'chumim" before the sabbath, i.e. that he places… two meals' food, thereby acquiring sabbathhood at that location when the sabbath starts, meaning that we look upon the location where he left the eruv as if it's his house for this sabbath…

My kid asked: Why is it possible for someone to make both an eruv chatzeros and an eruv t'chumin? It's setting his residence in two different places for the same sabbath and shouldn't work. [I might add that the same applies to making two eruve chatzeros.] We've never heard that's impossible.

Answer 1

To address your bracketed query regarding making two eruvei chatzerot, Aruch HaShulchan, Orach Chayyim 372:15 writes:

בית העומדת בין שתי חצרות, שכל אחת עירבה לעצמה והוא עירב עם שתיהן - יכול לטלטל לכאן ולכאן כל דבר. ואין לומר איך אדם דר בשני מקומות, דאין זה שאלה, דכל אדם יש לו רשות לדור ולאכול בכמה מקומות, וכולם חשובים אצלו דירות.‏

A house which is in between two courtyards, each one having made its own eruv, and [the inhabitant of this house] makes an eruv with both of them, he may carry anything to both courtyards.

Don't ask, "How can someone live in two places?" This is no question, because every person can live and eat in multiple places, all of which are considered his houses.

As far as your primary question regarding creating both an eruv techumin and eruv chatzerot, I would posit that the same holds true. One can create a residence at the time shabbat starts in the place where one places one's eruv techumin, while simultaneously having another residence (to be used later on during shabbat) in the courtyard for the purposes of creating an eruv chatzerot.

Answer 2

There is a big difference between them. Eruv t'chumin establishes your residency for this shabbos. While, eruv chatzeros establishes your ownership or actually gives up your ownership rights for other to use. Its easier to image when you are owner of 2 houses. You decide to spend the shabbos in house A but your neighbors from house B are asking if their kids can play in your backyard of house B?
So your eruv t'chumin is in house A while the neighbors from house B need you to relinquish your ownership rights for them to carry in your rightful property there. The best example is a bungalow colony where there are communal areas such as playground and all the owners have part in it and therefore no one can carry from their private bungalow to a shared space. The way around is to create eruv chatzeros by relinquish their personal rights to the communal space and thereby making into 1 owner property.