When you type
./program
The shell tries to execute the program according to how it determines the file needs to be executed. If it is a binary, it will attempt to execute the entry subroutine. If the shell detects it is a script, e.g through the use of
#!/bin/sh
or
#!/bin/awk
or more generally
#!/path/to/interpreter
the shell will pass the file (and any supplied arguments) as arguments to the supplied interpreter, which will then execute the script. If the interpreter given in the path does not exist, the shell will error, and if no interpreter line is found, the shell will assume the supplied script is to executed by itself.
A command
sh program
is equivalent to
./program
when the first line of program contains
#!/bin/sh
assuming that /bin/sh is the sh in your path (it could be /system/bin/sh, for example). Passing a binary to sh will cause sh to treat it as a shell script, which it is not, and binary is not interpretable shell (which is plain text). That is why you cannot use
sh program
in this context. It will also fail due to program being ruby, awk, sed, or anything else that is not a shell script.