Please help me determine if the new shoots from the base of my new roses are suckers or the actual rose. The potted rose is Honorine de Brabant and the planted rose is Lady in the Mist. Thank you! :)

In the 2nd photo, the lower limb appears to be growing below the graft joint. I'm guessing it might be a sucker. I can't see it well enough to guess on the one in the ground. I don't know about your specific roses, but sometimes the growth is different on the root stock than on the grafted part of plants. Are the leaves the same shape? Does the new growth emerge the same way? Even the rate of growth can be an indication sometimes. Maybe someone else will know.

I think that there are not idle shoots, Rosa 'Honorine de Brabant, Class: Bourbon similar to the old English, they have fine leaves, slender shape of the spear, light green red lined.
for the cultivation in pot, it is necessary to use special fertilizer, less nitrogen content, increased content of phosphorus and potassium, similar to the petunia or pelargonia,

This question was answered in the Rose Forum. Neither plant is grafted, so there's no possibility of suckers from the rootstock. The photos simply show nice new growth on two healthy own-root roses.