immediately / at the same time
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immediately
Expresses that something happens or should happen without delay, directly, or immediately. It is often somewhat more formal than the word 'sofort' (immediately).
Nachdem er den Brief gelesen hatte, antwortete er sogleich.
After he had read the letter, he replied immediately.
The word is composed of 'so' and 'gleich'. This combination reinforces the idea of immediacy—something happens 'sofort' (immediately).
Als er den Anruf erhielt, machte er sich sogleich auf den Weg.
When he received the call, he immediately set off.
As an adverb, 'sogleich' (immediately) can stand in different positions in the sentence. If it stands in position 1, the verb follows directly (inversion).
Sogleich begann der Film.
Immediately, the film began.
'Sogleich' (immediately) is mainly used in written language or in a formal, elevated style. It often sounds somewhat more formal or literary.
Der Redner betrat die Bühne und begann sogleich mit seiner Ansprache.
The speaker stepped onto the stage and immediately began his address.
The meaning 'gleichzeitig' (at the same time) is very rare today and is considered outdated. You will find it almost only in old literature or in very elevated texts.
Er war ein großer Künstler und sogleich ein Mann von Welt.
He was a great artist and at the same time a man of the world.
immediate / same
'gleich' and 'sogleich' both mean that something happens very soon or without delay. 'gleich' is much more natural in everyday language and fits almost any conversation. 'sogleich' has the same basic meaning, but sounds more formal or somewhat elevated. You are more likely to hear it in announcements, polite situations, or written texts. If you are speaking normally with friends, 'gleich' is usually the better choice. If the sentence should sound a bit more official, 'sogleich' fits well.
Der Mitarbeiter bringt Ihnen die Unterlagen sogleich.
The employee will bring you the documents immediately.
Im Urlaub gehen wir gleich nach dem Frühstück einkaufen.
On vacation, we go shopping right after breakfast.