[Jackyquah]

I buy two book to learn japanese.
-te form for :
v-verb : suffix -ru is replaced by -te (-て)
c-verb : suffix -u,-tsu atau -ru is replaced by -tte (-つて)
suffix -bu, -mu atau -nu is replaced by -nde (-んで)
suffix -su is replaced by -shite (-して)
suffix -ku is replaced by -ite (-いて)
suffix -gu is replaced by -ide (-いで)
other verb : suru (する) become shite (して)
kuru (くる) become kite (きて)
iku (いく) become itte (いつて)
adjective-i : suffix -i is replaced by -kute (-くて)
adjective-na : is added with -de (-で)

the problem is when -te form is followed mo have different description.
in first book, it's said that it's for conditional.
example : Ano kaban ga takakutemo, watashi wa kaimasen.
meaning in english : if that bag is expensive, I will not buy it.
in second book, it's said that it's to express something that is against the cause/requirement/reason for the following sentence.
example : ashita ame ga futtemo, watashi wa Kooen e ikimasu.
meaning in english : Although tommorrow is raining, I will go to park.

which one is correct ? or is both of them correct ?