Difference between paired-end, mate-pair and long read I writing here because I have some questions for you.
I wondered what the essential differences were between paired-end, mate-pair and long read?
for me mate-pair and classic paired-end are both paired-end reads, with the difference that :

For classical paired-end: the insert size on classic paired-end is
smaller (about 500bp)
while the insert size of mate-pair is much longer (several Kb)
which allows to join the contiguous between them especially is it?

In revenge for the long-reads, I imagine that they are simply reads that are synthesized with a large read size but that do not allow like the maite-pair to make junctions between contigs?
They are all very different in separate regards, but they all refer to different wet-lab and sequencing protocols/technologies.
First, PE (paired end) reads are typically short (50-300) reads, most often Illumina HiSeq, MiSeq or NovaSeq protocols. Both pairs originate from a single fragment which is sequenced from either end:
------&gt; PE1
-------------------------------- Fragment
                         &lt;------ PE2
       ^^^^^^^^^^^^^^^^^^        Insert

In contrast mate pairs arise from a fragment that is circularized before sequencing. Now imagine the fragment is circularized:
                     -----&gt; MP1
....--------------------------------.......
          MP2 &lt;-----
                    ^Circularized (joined) here

Long reads typically refer to PacBio or Oxford nanopore data, with very long reads lengths (up to several hundred kb).