What is the difference between lm(data~time) and tslm(data~trend)

Question

I observed that the results for both methods are different. Why is this? I know what is going on on lm, but can't figure out what happens under the hood at tslm.

> library(forecast)
> set.seed(2)
> tts <- ts(100*runif(1200)+seq(1:1200)*0.1, frequency=12, start=c(2000,1))
> lm(tts~time(tts))

Call:
lm(formula = tts ~ time(tts))

Coefficients:
(Intercept)    time(tts)  
  -2400.365        1.225  

> tslm(tts~trend)

Call:
tslm(formula = tts ~ trend)

Coefficients:
(Intercept)        trend  
    48.9350       0.1021  

Answer 1

Run the following three commands:

predict(lm(tts~time(tts)))
predict(tslm(tts~time(tts)))
all.equal(predict(lm(tts~time(tts))), predict(tslm(tts~trend)))

You will convince yourself that they are identical. if the outputs are identical, then the X variable of the lm regression, i.e.

time(tts) 

must be a linear transformation of

trend

The easiest guess:

tmp <- time(tts)*12
lm(tts~tmp)

Has the same coefficient as the tslm coefficient. So trend is just

12*time(tts)

I.e. trend is the (integer) count of the time passed since year 0, in months. time(tts) is the count of the time passed since year 0, in years.