There are many, many species of honeysuckle but only a few are invasive. Shrub forms are different species from vining forms and the only explanation I can offer as why they may pop up together is that both produce a fruit that is beloved by birds and other wildlife who do their best to spread these plants around. So removing just the vines will not have any impact the shrubs and vice versa.

In this case, they are invasive GG48. The shrubs could be Lonicera morrowii or L. maackii or L. tatarica or L. x bella. All are invasive in the northeast and at least some in the great lakes and midwest regions. Japanese honeysuckle (Lonicera japonica) is a vine which also qualifies as invasive in the northeast and maybe the midwest. I pull at least 2 of the 4 regularly but it is unending.

I often find a mix of invasives in similar spots under favorite bird perches for the reasons GG48 mentioned.

I'm not arguing that the OP's honeysuckles are invasive. I am very aware of this issue. It was just the impression given from the posting that the shrub honeysuckle and the vining honeysuckle were invasive by definition when there are nearly 200 species of honeysuckle and only a scant handful are considered invasive. In my area, shrub honeysuckle would most likely refer to Lonicera nitida or Lonicera pileata, both non-invasive landscape ornamental evergreen shrubs.

I also wanted to clarify the OP's supposition that the vining forms and the shrub forms are not the same species and the presence of one does not guarantee the presence of the other.