The Black & Decker PHV1810 is the newer model while the PHV1800 is an old model.

PHV1810 vs PHV1800
images from manufacturer

Charging:
The Black & Decker PHV1800 comes with a wall mount charging base while the PHV1810 does not include one, you have to plug a cord into it to charge.

Suction:
The PHV1810 has only one suction level while the PHV1800 has two suction settings: high speed for powerful suction and low speed for longer running time.
Users say that the suction of the PHV1810 cannot compare with the PHV1800, even the low suction setting of the PHV1800 is more powerful than PHV1810.

If you know more difference between PHV1810 and PHV1800, please share below.

P.S.
Black & Decker customer support say that the PHV1800 is identical to PHV1800CB.