Read about the differences between these two structural sections that often get mixed up.
Bridges and Middle 8s are two Structural Sections that can cause confusion. There are many different opinions on this but I will be sharing what I think on this subject.
My answer is actually very short. A bridge is a section that is used to get between two sections, it literally 'bridges' two parts. Because of this it is usually instrumental, or at least doesn't have any major lyrical content. By that I mean there might be some 'oohs' or repetition of existing lyrics or minimal lyrics. Bridges come in all sorts of lengths, sometimes they are just a bar or two and sometimes can span minutes worth of music.
A middle 8 on the other hand is generally more of a 'lyrical' based section. It is named this way because in traditional pop songs it comes at the middle of the song and lasts 8 bars. The original purpose of this was to break up a repetitive verse-chorus-verse-chorus strucure. As music has developed this has changed and you will find middle 8's at various points through the song at all sorts of lengths. It is almost like an extra verse that is completely different musically and lyrically to other previous sections.
So in summary, a bridge is a section that is used to get between other song sections and a middle 8 is similar to a verse/chorus.