Both of grammar are the same meaning: something has “just” finished/done?
-たて attaches to some verbs and forms so-called a no-adjective (noun).
Note that this refers to the quality of the described object; the object itself has to be new or fresh. You can say 印刷したての本 but usually not 読みたての本, because the book itself does not have to be new in the latter case.
-あげる that appears in many compound verbs means either thoroughly or to upper direction, both of which roughly correspond to "up". But it does not mean just per se, while it tends to be used with another phrase that means just.
- 小説を書き上げた。 I finished writing a novel.
- たった今小説を書き上げた。 I just finished writing the novel.
- 太陽を見上げた。 I looked up to the sun.
There are other expressions that enable you to say "I have just [verb]." See: Verbs + ところ / Verbs + とこ / Verbs + ばかり