Is there any difference between square meter and meter square?

When you are talking about a unit of area, you want to say "square meters".

For example, if I have a floor that is 2m by 4m, it has an area of "8 square meters".

The confusion comes in by how that is represented as units. We would write "8 square meters" as 8 m².

If you refer to that as "8 meters square" it could be misinterpreted as a square that is 8 meters on each side (or 64 square meters).

1 meter square refers to a specific shape (a square) with sides of 1 meter.

1 square meter refers to an area (of arbitrary shape) equivalent to a square 1 meter on each side. So a rectangle that was 2m by 0.5m has an area of 1 square meter.

tl;dr The unit of area is a square meter, but is written as "m²". Don't read that as meter square because that term isn't well defined.

No, but there is a difference between two (or more) square meters and meters square.

"25 square meters" = 5 meters x 5 meters.

"25 meters square" = 25 meters x 25 meters.