They didn't do it in the way that we do now 和They didn't do

前者是定语从句,way作先行词,关系代词在从句里作方式状语,可以用in which,也可以用that,或者把它省略掉,如：
The way in which he ran was funny。
I couldn't help laughing at the way in which he pronounced the sound /r/。
后者是状语从句,the way本身可以引导状语从句,如：
Do it the way you were taught。
A lot of people speak English the way I do。
希望我能帮助你解疑释惑。