What is the difference between declare and typeset

In bash, typeset and declare are exactly the same. The only difference is that typeset is considered obsolete.

typeset: typeset [-aAfFgilrtux] [-p] name[=value] ...
    Set variable values and attributes.

    Obsolete.  See `help declare'.

The man page even lists them in the same breath:

declare [-aAfFgilrtux] [-p] [name[=value] ...]
typeset [-aAfFgilrtux] [-p] [name[=value] ...]
    Declare variables and/or give them attributes.

typeset is portable to some other shells, for example, ksh93. If you are aiming for cross-shell portability, use typeset (and make sure that the way you are calling it is portable). If you don't care about such portability, use declare.

I know a case where declare is useful to avoid the evil eval : variable indirection :

$ var=foo
$ x=var
$ declare "$x=another_value"
$ echo $var
another_value