Question: To save board space I want to replace relays with SSRs where possible. Most of the relays I use don't need to carry a lot of current and don't to switch high voltages. Mostly slow 24V digital signals to connect to other devices working at other potentials.

Classically relays are use for this, but SSRs would be a lot more convenient.

The question is: Can SSRs designed for DC voltages switch currents at arbitrary potentials (obviously < isolation voltage). There is really not much information about this.

Answer: 
The TP4056 uses a **[pass transistor](https://www.electronics-notes.com/articles/analogue_circuits/power-supply-electronics/linear-psu-series-regulator-circuit.php)** to regulate the charging voltage / current to the battery.

That pass transistor is controlled in a **linear** way, meaning a **gradual** on/off control. So the pass transistor can be fully on, fully off or any state in between (having a certain resistance).

A different type of regulator is the **switched** regulator where the pass transistor is **switched** so it can be **on** or it can be **off**. There is no state in between (like a high resistance state).

> 
> Or is it linear as in "linear power supply vs switching power supply"?
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> 
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Yes it is.
It is linear as in *linear power supply*. It works by using a pass element, whose resistance is modulated so either constant current or constant voltage is supplied to the battery, charging it correctly.

**Update:**
A pass element in a linear regulator is some form of a transistor, which is operated in its "linear"/"ohmic" region, so it is neither fully conducting ("on"), nor fully off. The magic is in the biasing circuit (the rest of the linear regulator) which provides suitable voltage or current to the gate or base terminal of the transistor, so the required amount of current is *passed* from input to output.