Is there any difference between Airbus and Boeing on yaw damper technology?
The difference is more between conventional flight controls vs. fly-by-wire rather than Airbus vs. Boeing.
Both Airbus and Boeing used separate yaw dampers in their non fly-by-wire aircraft, which applied their commands with separate actuators to the rudder control servos, without feedback to the mechanically linked rudder pedals in the flight deck. The exact details will differ for every aircraft of course, but the general design is quite similar. Consider e.g. the Airbus A310 and the Boeing 747:
Airbus A310:

The rudder is controlled by 3 actuators, which are commanded by a
single cable run from the rudder pedals. Rudder artificial feel is
provided by a spring-loaded rod.
Additional inputs to the rudder come from:

the rudder trim, and
the 2 yaw dampers.

[...]
The yaw damper ensures the following functions:

dutch roll damping
turn coordination which becomes active if sufficient control wheel deflection is applied [...]
yaw compensation in case of engine failure, provided the AP is engaged in CMD with SRS (takeoff) or GO AROUND mode annunciated on
FMA.

Yaw damper command is transmitted to the rudder but there is no
deflection feedback sent to the rudder pedals.


(Airbus A310 FCOM - Flight Controls - Rudder Control)
Boeing 747-400:

Yaw Dampers
Two independent yaw damper systems operate continously in flight to
improve airplane directional stability and provide turn coordination.
The upper and lower yaw damper actuators are powered by hydraulic
systems 3 and 2 respectively. Yaw damper inputs do not result in
rudder pedal motion.


(Boeing 747-400 FCOMv2 9.20.9 - Flight Controls - System Description)

On the other hand, fly-by-wire aircraft usually integrate the yaw damper logic into the fly-by-wire commands sent to the actuators. Consider e.g. the Airbus A320 and the Boeing 777:
Airbus A320:

Electrical Rudder Control
The yaw damping and turn coordination functions are automatic. The
ELACs compute yaw orders for coordinating turns and damping yaw
oscillations, and transmit them to the FACs.
Rudder Actuation
Three independent hydraulic servojacks, operating in parallel, actuate
the rudder. In automatic operation (yaw damping, turn coordination) a
green servo actuator drives all three servojacks. A yellow servo
actuator remains synchronized and takes over if there is a failure.
There is no feedback to the rudder pedals from the yaw damping and
turn coordination functions.


(Airbus A320 FCOM - Flight Controls - Description)
Boeing 777:

The yaw control law contains the usual functionality employed on other Boeing jetliners, such as the yaw
damper and rudder ratio changer (which compensates a rudder command as a function of airspeed).
However, the 777 FBW rudder control system has no separate actuators, linkages, and wiring for these
functions, as have been used in previous airplane models. Rather, the command for these functions are
calculated in the PFCs and included as part of the normal rudder command to the main rudder actuators.
This reduces weight, complexity, maintenance, and spares required to be stocked.

(Boeing B-777: Fly-By-Wire Flight Controls 11.8.2 - Yaw Control)