"Afterwards" has the same meaning as "after" but its usage is much more limited.
Only "after" can be used in these sentences:
"I will speak to you to after lunch." [preposition]
"After I speak to you, I will speak to him" [conjunction]
"After speaking to you, I will speak to him" [preposition]
You can use either here but "after" is sometimes considered too informal.
"After/Afterwards, I will speak to you" [conjunction] or end of sentence
"I will speak to you after/afterwards" [conjunction]
In this case "After/Afterwards, refers to the thing you mentioned in the previous sentence.