In addition to Glenn-san's explanation regarding the difference between two types of verbs, ta-form of action verbs expresses past tense, whereas ta-form of change-of-state verbs expresses being in a state of completion. Or, the latter case, change-of-state verb, is more likely close to present perfect tense.
飲む; action verb
牛乳を飲んでいる。[Gyuunyuu o nondeiru.] → 牛乳を飲んだ。[Gyuunyuu o nonda.]
I am drinking milk. → I drank milk.
死ぬ; change-of-state verb
鳥が死んだ。[Tori ga shinda.] → 鳥が死んでいる。[Tori ga shindeiru.]
The bird has died. → The bird is dead.
*死んだ can be used as past tense depending on the context.
e.g.
昨日鳥が死んだ。
The bird died yesterday.
As for the verb 着る, 着ている can be used as both present progressive and present tense.
What I don't understand is, why didn't they say shiroi shatsu o kite ite aoi jiinzu o haite imasu? I mean, in the picture she is already wearing a white shirt. So why use kite instead of kite ite?
I'm not sure but "~していて、…" seems not to be able to be used as a simple paratactic use.
目を瞑っていて、彼女が来たのに気付かなかった。
Me o tubutteite, kanojo ga kita no ni kizukanakatta.
未成年なのにお酒を飲んでいて怒られた。
Miseinen nanoni osake o nondeite okorareta.
防弾チョッキを着ていて助かった。
Boudan-chokki o kiteite tasukatta.
バブルが崩壊するとわかっていて、避けられなかった。
Baburu ga houkaisuru to wakatteite, sakerarenakatta.
In the first three examples above, the coordinate clause explains why the thing/action in the main clause occurs, thus, ~て can be rephrased as ~たから. The last one expresses the adversative conjunction, same as ~たのに/たが.