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Most glues are capable of bonding 2 pieces of paper together and so it is more then a matter of application.
A plastic usually abbreviated as PVA. A colourless transparent solid, it is usually used in adhesives, which are themselves also referred to as PVA or PVA adhesive.
The main benefit of this type of glue with paper is that it forms a very strong joint and is easy to use.
As paper is porous the glue will seap into the paper and can discolour the paper.
Also, this glue is slow drying and so you will have to leave the glue to dry or apply a clamp to hold the parts together whilst you continue to work.
For a scrapbook type of application then a Pritt stick works very well and is quite clean to use.
The downside is that these type of glues tend to dry out over time and the joint becomes brittle, then any flexing of the paper results in the joint failing.
This is not exhaustive and so please do email me if you have a question or even better an answer.