"A man and a boy"
Translation:Ein Mann und ein Junge
einen is masculine accusative -- but there is no context that would require this to be accusative.
In the absense of any context, we translate in the nominative case -- where ein is used before both masculine and neuter nouns.
ein Mann, ein Junge (masculine), ein Mädchen, ein Kind (neuter)
a and ä are different letters, just like l and t are different letters -- a t is not just "an l with an accent".
So yes, there are certain times when you use a and certain times when you use ä.
For example, Mann (man: singular) always has a, Männer (men: plural) always has ä. Like how in English "lip" (on your mouth) always has l and "tip" (point) always has t.
It's part of the spelling of the word -- and, as with lip/tip, can make the difference between two completely different words. An example in German is schon (already) versus schön (beautiful).
And as with l/t, a/ä stand for different sounds.