Minor correction here.... You were right the first time... Repeaters work by using paired frequencies, and they retransmit RF. One pair if it's simplex (only one person can talk at a time), two pairs if it's duplex (works like a telephone). It's easiest to explain with the simplex - the incoming transmission is received on frequency X, then rebroadcast on frequency X+Y, where Y is the offset, a predetermined shift in the frequency (depending on the frequency range that the radios operate on). So if the radio is running at 825MHz, with an offset of 25MHz, then the incoming transmission would be rebroadcast at 850MHz (on a + offset) or 800MHz (for a - offset). Whether it's a +/- offset is also determined by the system, and the radios are programmed accordingly.
A full duplex system works slightly differently. In reference to the base station, there's a "talk" frequency and a "listen" frequency (these are reversed in the field radios). The repeater works exactly the same, but with a total of 4 frequencies instead of 2.
What they call "simplex" around here is a non-repeated frequency: tx and rx frequency is the same.
Usually, that is our "tactical" or mobile-to-mobile channel used for comm on an incident. The state owns multiple of these channels which means that different divisions or different incidents can have their own channel with little overlap to other incidents because of limited range.
When we want to talk to the county dispatch (or a neighboring county), we have to use the repeated channel but for incident operations you want to keep the repeater clear for other traffic.
Anyway, the whole point being (again!) that our county has a base channel (non-repeated) for LE that is encrypted now, which only covers the county seat and nearby. Anywhere else in the county (2500 sq mi and mostly mountains), LE has to use the non-encrypted repeaters which are
also used by fire, EMS, road crews, school buses, etc.