Difference between "remain" and "be left"

Solution 1:

An ace of spades remained.

This places the emphasis on the fact that an ace of spades is still there after some other cards were removed.

An ace of spades was left.

This places the emphasis on the sequence of actions that led to other cards being removed, but not the ace of spades.

More context is necessary to choose the best answer, but both are grammatically correct.

Solution 2:

If the subject is a person, the difference is one of volition:

If you say:

I remained on the desert island.

then it was probably your choice; you wanted to stay there.

If you say:

I was left on the desert island.

then maybe the ship left without realizing you weren't aboard, or maybe you were marooned there by your mutinous crew. But either way, it probably wasn't your decision.

If the subject is the ace of spaces, then there really isn't any difference.

Solution 3:

There is no difference between the two, to call a spade a spade!