Hello and thank you for your question. The vines in your images look to be the same species, a non-native invasive called porcelain berry. The leaf shape can vary, from heart shaped with no lobes to heart shaped with two lobes, separating it into three points with coarse margins. Our native wild grape can look similar, but the woody stem of grape has shredding bark, whereas porcelain berry does not. 

The berries in your first photo are still green but as they mature they will turn shades of purple, blue, white, yellow and pink. As pretty as the berries are, they spread aggressively, both by seed through animal dispersal and by root sprouts. Seeds are viable for years and years in the soil, and once they sprout the vines can grow up to 15' in one season.

For management, removal of small seedlings is crucial. Hand pulling, especially in moist soil, is not difficult when they are small. Once they grow larger, the woody, forked root system makes hand pulling more challenging. Cutting near the base and treating the cut stump, and any regrowth, with an herbicide is a good method for control. Do not compost any berries, instead bag and dispose of them in the landfill.

Repeated treatment and control may be necessary if additional seeds remain in the soil, or if a root fragment was not removed or killed off. Keep an eye on the area for a few years post-control to be sure it's taken care of.

Here is some additional information for your reference:
https://extension.umd.edu/resource/invasives-your-woodland-porcelain-berry

Please let us know if we can be of further assistance.

You’re welcome.