Understanding the Math of Segmented and Splines2 packages.

Question

I was trying to teach myself the math behind what produces the slope and intercept of a segmented variable in the segmented package using the plant data set. My plan was to run a model through the segmented package, produce the slopes and intercept using the slope and intercept commands and compare to summary output to the summary output of splines2 package.

I notice then that both outputs from both packages summary functions were not the same.

My questions are thus:

1. Am I wrong in assuming the segmented function in the segmented package fits a spline with a degree of 1 similar to using the bSpline function with a degree of 1 in the splines2 package?
2. Is there a way to get the slopes and intercept for each variable (as opposed to the orthogonal spline in the summary output) from teh splines2 package? Even hard coding the steps would nice to know.

Here is the code I used to try and do this task:

library(segmented)
library(splines2)

data <- data("plant") 

#run glm
plant_glm <- glm(y ~ time, data = plant)
#run segmented model
plant_segmented <- segmented(plant_glm, Z = ~time, psi = c(366.5))
#get summary, slope, and intecept
summary(plant_segmented)
slope(plant_segmented)
intercept(plant_segmented)

#Run BSpline model
spline_model <- glm(y ~ bSpline(time, degree = 1, knots = 366.5),data = 
plant)
#get bSpline summary
summary(spline_model)