hinterher
afterwards
After that in time; at a later point.
Wir gehen jetzt ins Kino und könnten hinterher noch etwas essen gehen.
We're going to the cinema now and could go for something to eat afterwards.

afterwards / behind
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afterwards
After that in time; at a later point.
Wir gehen jetzt ins Kino und könnten hinterher noch etwas essen gehen.
We're going to the cinema now and could go for something to eat afterwards.

The adverb is made up of 'hinter' (behind) and 'her' (movement toward the speaker). This structure illustrates the basic meaning of following, whether spatially or in time.
Lauf nicht so schnell, ich komme ja kaum hinterher!
Don't run so fast; I can hardly keep up!
As an adverb, 'hinterher' can stand in different positions in the sentence. If it is in position 1, the verb follows directly after it (inversion). It can also stand in the middle of the sentence.
Hinterher haben wir alles verstanden.
Afterwards, we understood everything.
The expression 'hinterher sein' means to be behind. It is often completed with the preposition 'mit' and the dative to indicate what someone is behind with.
Ich bin mit meiner Arbeit total hinterher.
I'm totally behind with my work.
The spatial meaning ('hinterdrein', behind/after someone) is usually used with verbs of movement such as 'laufen' (to run/walk) or 'fahren' (to drive/go). The temporal meaning ('danach', afterwards) refers to the sequence of actions or events.
Erst die Arbeit, hinterher das Vergnügen.
First work, then pleasure afterwards.
to / after / according to
'nach' and 'hinterher' can both express that something comes later or follows. 'nach' is a preposition and is used with a noun or pronoun, for example 'nach dem Essen' (after the meal) or 'nach mir' (after me). 'hinterher' is an adverb and stands on its own, or refers to something that is already known. It can mean 'afterwards' in a time-related sense, but also spatially: someone runs after another person. Learners confuse these words because both can express a sequence. A practical tip: if a noun follows directly, you usually use 'nach'. If you generally mean 'afterwards' or 'after / behind someone', 'hinterher' fits better.

Wir besprechen den Plan jetzt kurz, die Details klären wir hinterher.
We'll briefly discuss the plan now; we'll clarify the details afterwards.
Nach dem Gespräch gehen wir kurz an die frische Luft.
After the conversation, we'll go outside for some fresh air for a moment.