The functions of 在 and 着 are only superficially similar, and only when we translate into English. They can both be represented by -ing sometimes. German, for example, does not have this crazy -ing form and therefore you cannot translate using an -ing form, but you can of course translate.
What is known as the Present Tense in English is almost never used to represent the present time and perfectly indicates continuous action: Example: I live in China.
The translation of combinations of 在 and 着 depends entirely on the context and to some extent on the translator. A one-word translation for 在想 is 'think'.
我在想:I think / (German: Ich denke. (There is no 'I am thinking' in German.))
我想着:I think / Ich denke
每天都在下雨:It rains every day.
每天都下着雨:It rains every day.
You can use 在 and 着 together:
他在想 / 他在想着,各种影响能不能相互抵消。
You can use 在 when you are talking about the past, so don't assume it only applies to the present: (I borrowed moiaussi06's sentence and changed it a bit. Bonjour Moiaussi! Me too is a strange name.)
我当时在穿着很厚的衣服,所以我的胳膊动不了。(当时 puts this event clearly in the past.)
There seems to be some confusion here about 'wearing' and 'dressing'.
Phone rings, you answer.
Q: 你在做什么?
A: 我在穿(着)衣服。 I am getting dressed
Phone rings, you answer.
Q: 你在穿着什么衣服?
A: 我在穿(着)红色的外套。 I am wearing a red coat.