ggplot works most effectively with data in "long" format. In the code below, we convert your data to long format using the gather function and then map the new key column (marking whether the data values came from expl or use) to colour. You haven't provided a data sample, so I'm inferring what your data probably looks like, based on the code you provided.
In addition, for geom_smooth (or, equivalently, stat_smooth) to work, the outcome variable must have two categories and must be coerced to numeric values (if they aren't already numeric), preferably on a 0/1 scale, as described here. I haven't done that below, but I can be more specific if you provide a data sample.
library(tidyverse)
bxint %>%
gather(key, value, expl, use) %>%
ggplot(aes(seq, value, colour=key)) +
geom_jitter(height=0.1) +
geom_smooth(method=glm, method.args=list(family="binomial"))
To get different colors for the points and the smoother lines, we use a point marker with separate border and fill colors. Then we can set the fill for the markers separately from the color for the lines:
bxint %>%
gather(key, value, expl, use) %>%
ggplot(aes(seq, value, colour=key, fill=key)) +
geom_jitter(height=0.1, shape=21, stroke=0) +
geom_smooth(method=glm, method.args=list(family="binomial")) +
scale_fill_manual(values=hcl(c(15,195), 100, 40)) +
scale_colour_manual(values=hcl(c(15,195), 100, 65))