StringCases: return list of outputs for each of several patterns

Question

According to the documentation,

StringCases[{s1, s2, ...}, p]

returns

{StringCases[s1, p], StringCases[s2, p], ...}

but, oddly enough,

StringCases["string", {p1, p2, ...}]

returns the results which match any of the patterns $p_i$, which is essentially equivalent to

Union[{StringCases["string", p1], StringCases["string", p2], ...}]

Is there a way to modify StringCases["string", {p1, p2, ...}] to return just

{StringCases["string", p1], StringCases["string", p2], ...}

in an analogous manner to how StringCases[{s1, s2, ...}, p] does it?

One alternate way to get the same output would be

Through[Table[StringCases[#, p[i]] &, {i, n}]["string"]]

but I was curious if there was another way.

Answer 1

Maybe

p = {"abc", "cd"};
string = "abcdabcdcd";

StringCases @@@ Thread[{string, p}]
(* {{"abc", "abc"}, {"cd", "cd", "cd"}} *)

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Original post:

StringCases[string, p, Overlaps -> All]
(*  {"abc", "cd", "abc", "cd", "cd"} *)