In star system, single phase consumers are connected between a line and neutral but are there any single phase devices connected between two phases (would that even be considered a single phase device?)?
In the USA, some residential and commercial services are supplied with 120/208 volt service. The 120 V phase to neutral is used for standard wall receptacles and lighting. Phase to phase 208 V is used for single-phase kitchen stoves, water heaters, clothes dryers and motors in heating and air-conditioning units. Small single-phase motors are widely available for 208 volts.
In the rest of the world, where 220-230 V is supplied for wall outlets and lighting, the phase to phase voltage is 380-400 volts. Single-phase motors for that voltage level would be quite unusual. It seems unlikely that other loads would be served at that voltage, but it is certainly possible.
I have an old Oxford stick welder that can be run between phases or in phase to neutral mode, between phases (400V input tap) gives a better weld especially when the supply cables are a bit on the long side.
So, yea, kit designed for phase-phase exists, but I think the actual intended use in this case was to allow welding when a deta supply was all that was available.
There are voltage testers, which determine the direction of rotation. They are connected to 2 of the 3 phases. ("Phase Sequence Test")
However, this is probably not what you consider a "device".
Many condo buildings are served by a three phase 120/208 transformer. The lobby air conditioner would be 120/208 3phase and would need all three 120V legs. The condo units would have 120/208 1 phase and would need two 120 legs and a neutral. The single phase loads would need one of the two 120V legs and the neutral. The water heater would normally need just the two 120V legs for 208V and no neutral. The water heater is considered to be single phase but is connected to two phases. The ovens, air conditioners and stove tops, which are also considered single phase, would also need the two 120V legs but could also include a neutral if they needed 120V for a clock/timer, etc.
Volts are volts. In industrial applications, many protective relays and other devices are powered from single phase line-to-line (typically) or line-to-neutral taken off the 3φ coming into the building. As long as you know the voltage phase relationship to whatever you need to measure with the device (or if it doesn't matter because you're not measuring anything) and can properly configure the device, you can typically power these devices off of whatever single phase you'd like.
This is why you'll often see protective relays that come in 120 Vac and 208 Vac variants (among others); these could both be used in a 3φ+N system 208 Vac system, but wired up differently. Sometimes it comes down to the device preferring (but not needing) neutral for best performance, or the customer mis-ordering and not having the time or money to replace units already in the field.