What are the name of these plants?
This plant looks like Nandina domestica, Heavenly bamboo. Nandina is listed as a Tier 2 Invasive Plant in Maryland, which means it has the potential to be invasive, as it is invasive in some surrounding areas, and care should be taken to watch it carefully for invasion. It must legally be labeled as a Tier 2 by nurseries. We do not recommend planting it.
Here is more information from the MDA http://mda.maryland.gov/plants-pests/Pages/maryland_invasive_plants_prevention_and_control.aspx
Can you name a less evasive plant that looks similar ( with red/green leaves and berries)?
Where are you planning to use it? What are the soil, sun and size conditions and limitations there?
There are some smaller hybrid Nandinas (Firepower, etc) that still get that lasting firery red top foliage that don't berry.
Ilex verticillata, or winterberry holly is a deciduous small tree that gets great berries that last through winter.