What's the difference between " " and " "?

One is non-breaking space and the other is a regular space. A non-breaking space means that the line should not be wrapped at that point, just like it wouldn’t be wrapped in the middle of a word.

Furthermore as Svend points out in his comment, non-breaking spaces are not collapsed.

The entity   produces a non-breaking space, which is used when you don't want an automatic line break at that position. The regular space has the character code 32, while the non-breaking space has the character code 160.

For example when you display numbers with space as thousands separator: 1 234 567, then you use non-breaking spaces so that the number can't be split on separate lines. If you display currency and there is a space between the amount and the currency: 42 SEK, then you use a non-breaking space so that you don't get the amount on one line and the currency on the next.