The main difference between ている and past tense is that... ている is a state while the past tense is an action.
ている is very simple. It's basically the moment when someone did a verb (past tense), receive a change in state, and the result can be seen clearly as a consequence of the verb.
食べている I am eating
notice that here the action 'eat' has been done. The speaker is in the state of eating as a consequence of doing the verb eat and start on the moment after the speaker bite, chew, and swallow. We regard this as progressive verb because as you did the verb, it is continuous.
落ちている It's on the ground
Here, you don't say that this means it is falling. Now imagine a coin is falling in the air from a table in midair. This coin hasn't done the verb 'fall', after all if this coin has done it, then we'd say the past tense (fell) while it is in the midair (which is weird). Here the coin has fallen (and we can see the state : on the ground).
verb + ing doesn't always mean progressive verb because some are instantaneous and doesn't possess the continuous manner (like the verb 'fall'). This type of verbs then, when changed into + ing, will mean that it is on the progress that the verb is going to be done (but not yet done... it's like on it's way to do the verb). (not the progress after the verb had begun).
死んでいる he's dead
Here's another example... we don't say, "he's dying". Because if we did, it means that the guy is still breathing, minutes away for what awaits him, where he'll die sooner or later. And that means the verb "die" hasn't been done.
開けている I have opened (door/window) [emphasizes the state of the opened ....]
閉めている I have closed (door/window) [emphasizes the state of the closed ....]
開いている The .... is open.
お腹が空いている My stomach is empty (hungry)
怒っている (I, you) am/are angry
生きている I'm alive
結婚している we are married
作っている I have made ... [Emphasizes the state]
If you want to say "dying or falling" then you can just use the future tense... (I think?)
死ぬ I am going to die (I'm dying)
The motion verbs are included in the latter. When we say "going", we haven't done the verb "go" (we haven't arrive yet). So if you can say it in the past tense... then you can use ている for this class of verbs (I went to Japan --> you
can say 日本に行っている). When you use ている, it means you are still in Japan. However if you use 行った, you might or might not be on Japan at the moment of saying.
Japanese has a lot of ways to say things. like 終わっているところ and 行く時 or just use the plain form with additional context or time specifications when trying to express your so "Progressive form of motion verb".
Related When is Vている the continuation of action and when is it the continuation of state?
to help you differentiate these 2, you may translate ている as 'has/have'. 家に帰っている --> I have gone home vs 家に帰った --> I went home. 帰った would be used if you already left the house (Like in school/office you say... "Yesterday I went home."). But you will probably see that most of the time ている is not translated as 'have/has' because we want to emphasize the change of state. Have/has' is more of an action. 分かっている (I have understand it... and therefore : I understand (state of understanding the matter). It is often used by the speaker to reassure the listener that the speaker is capable/going to be fine. 分かった is an expression that is commonly used when one hears something afresh and understands that (like when a teacher tell you what you should do, you reply in this manner). In English it is typically "Yes, I understand" and "Understood.". So as you can see, as you might wonder what's the difference between the present tense, past tense, and the progressive/resultant state (like 困る、困っている、困った) in the future for some words, take note that sometimes the differences rest on the type of/special words used which will give special expressions that no other words will give.
困る I'm troubled (expressing the speaker's annoyance)
困っている I'm troubled (State of being troubled, especially for over a period of time)
困った I'm troubled (modal た, when the speaker's expectation has matched or failed to matched reality --> this is not past tense!)
So you shouldn't be that worried. If you cannot differentiate the ている and past tense for a word (like 困っている and 困った) and they have the same meaning... it'll probably mean that the differences lies in the way of expressing and nuances. For these words, you will understand them as you receive more experience, familiarize with the words/sentences, and keep on studying Japanese. For now know that ている is a state (can be translated as 'has/have') and the past tense is an action.
戻っている have come back (therefore I exist in this location right now)
信じている I believe in ... (I have believed in... therefore I'm in the state of believing)