Black and Decker BDH2000PL and PHV1810 are 2 handheld battery powered vacuum cleaners. They are bagless and can be folded up for easy storage.
Below are some differences and similarities between them.

PHV1810 vs BDH2000PL
images from manufacturer

Battery:
The BDH2000PL uses 20v lithium ion battery whereas the PHV1810 uses 18v nickel cadmium battery.

Charger:
The BDH2000PL has a charging base whereas the PHV1810 come with no charging base but a standard charger.

Charging Time:
The BDH2000PL takes much less time to charge than the PHV1810.
According to the manuals, the BDH2000PL takes about 4 hours to recharge while the PHV1810 must be charged at least 9 hours.

Dust Bowl Capacity:
The BDH2000PL holds 15 oz. whereas the PHV1810 holds about 16.9 oz.

Weight:
The BDH2000PL is a bit lighter than the PHV1810.

Color:
The BDH2000PL is black with silver whereas the PHV1810 is white with blue.

Similarities:
Pivoting nozzle with multiple angles; charging indicator; removable and washable translucent bin; 35 air watts suction power; 3-stage filtration; washable filter; 2 year limited warranty; on board brush and crevice tool; cyclonic action.

Please share more info if you own these 2 Black & Decker hand vac.