Well, there are many ways to skin... I mean, to make an absolute encoder.
One is to have a codewheel (a glass disk etc.) marked with a distinctive pattern for its every position (512, 1024 or however many of them). This way, the readings are known any time within one complete revolution. That's a classical single-turn absolute encoder.
Such an encoder may be fitted fith a small set of gears, a battery and a simple electronics circuit. Now it becomes a multi-turn absolute encoder, capable of knowing its position within many revolutions - as long as the battery is good. These encoders are usually fitted with an input, allowing to zero the reading when closed and an output, going low when the battery is dead ("data valid").
Both these encoders provide the output in parallel format (8, 10, 12 and more outputs) and are more often coded in Gray, rather than binary code (PLC logic must do the conversion, which is simple).
Sometimes, an ordinary incremental encoder (two pulse channels shifted 90 degrees) are fitted with a battery that retains its readings in the motion control module the encoder is connected to (this is common practice in CNC and robot systems). This configuration can also be referred as an "absolute encoder", although, strictly speaking, this is not quite correct.
What you call a "sinecosine" encoder sounds awfully like a good old "resolver" to me. Instead of counting pulses, these devices rely on magnetic field and three-phase windings to output three analog voltages (like a small alternator, kind of). An electronic board the resolver is connected to, can measure these voltages at any given instant of time and to calculate true position based on that. So this type of device will also give you the position readout within a single turn (if not geared).
Please correct me if I am wrong.