suggest (that) sb (should) do sth中“that“和“should” 都可以省略么

suggest (that) sb (should) do sth中“that“和“should” 都可以省略么
都可以省略了,是不是就有了suggest sb.do sth.从某种意义上..
是不是就可以说：
I suggest you play tennis.
也可以说
I suggest you playing tennis
有区别么