I am reading about aorist and preterite verb forms. It seems that they are both forms which express perfective aspect and past tense. Is the difference between them simply in differing terminology or are there semantic differences as well?
Unfortunately, a lot of linguistic terms are used ambiguously/differently, and the term "aorist" is one of them.
Usually, aorist is understood as a combination of perfective (aspect) and past (tense) (Plungian 2012). Preterite is a simple past, aspectually non-marked - thus, such combinations as Perfective Preterite and Imperfective Preterite are possible. Under this proposal, aorist is a kind of preterite (i.e. Aorist=Perfective Preterite).
I teach my pupils the matter like this (and I hope it’s useful for anyone who reads this thread):
Greek has three ways of representing actions (I’m leaving out future tense because it merely expresses tense).
 as actions in process or repeated actions – durative [all forms beloning to the præsens stem] e.g. θνῃσκ- = to be dying
 as (merely) completed or single actions pointing towards completion – completive [all forms of the aorist [stem]: (‘aorist’ and ‘aorist stem’ mean the same in this way of representing). θαν- = to expire one’s last breath
 as a result of actions – resultative [all forms of the perfect stem] τεθνα-/τεθνηκ- = to have died -> to be dead
Then I explain to them that this basic stem related meaning is conveyed in all forms belonging to that specific stem (durative/præsens, completive/aorist, resultative/perfect).
Then I explain that all these stems have present tenses, past stenses, participles, imperatives, subjunctives, optatives and infinitives.
The next thing I need to do is explain that the aorist doesn’t/can’t have a present tense, because the idea of ‘completedness’ and ‘present tense’ are incompatible. Another thing that needs to be clarified is the perfect present tense is something different than the perfectum of Latin, but usually soon after this they realise there are only three past/preterite tenses in Greek [imperfectum (ἔθνῃσκεν), aorist past tense (ἔθανεν) and plusquamperfectum (ἐτεθνήκει) – all marked by the augment].
So, not all forms belonging to the aorist (stem) express past tense (θάνοι τάχα καὶ ἡσυχῇ - may he pass away soon and peacefully, πολλὰ δῶρα βούλομαι σχεῖν – I want to get/have any presents, τὴν θύραν ἀνοῖξον – close the door, ἡσθήσομαι οἴκαδε ἀφικόμενος - I will be happy (after) having arrived home).
‘Aorist (stem)’ and ‘past’ only coincide in those verb forms that have the augment.
What distinguishes the Greek aorist tense from others past tenses is its denoting uninterrupted/non-continuing action: it is punctiliar, though the action in point of time can be lengthy, such as 'they fought against reach other'. 'Fought' in the aorist could be momentary or take years; but the action is singular and completed. The Greek perfect tense differs greatly from the aorist by including the idea that the result of the action abides. For example, "He is risen." Risen in the Greek perfect means He rose and remains risen. In the ancient Greek middle voice, the aorist adds the idea that the whoever took the action participated in the outcome.
I have heard the term preterite, although not usually applied to English. Still, I am aware that English does posses three past tenses: aorist which is also called the simple past, present perfect, and past perfect.
- Simple Past: I saw the movie.
- Present Perfect: I have seen the movie.
- Past Perfect: I had seen the movie.
So the Present Perfect adds an Auxiliary Verb. The Past Perfect is formed by conjugating that Auxiliary. This explination may not be 100% correct but the website Englishpage.com seemed to help me.