Differences between declare, typeset and local variable in Bash

• Difference between typeset and declare:

The former is more portable(e.g. ksh), while the latter is more preferable when portability is not a concern.

• Difference between declare(or typeset) and local when used inside a function:

The former implies the latter, but more powerful. For example, declare -i x makes x have the integer attribute, declare -r x makes x readonly, etc.

As far as bash is concerned, no, there is no difference. In fact, the manpage has them share the same definition

declare [-aAfFilrtux] [-p] [name[=value] ...]
typeset [-aAfFilrtux] [-p] [name[=value] ...]
Declare variables and/or give them attributes. If no names are given then display the values of variables. The -p option will display the attributes and values of each name...

I also found this little tidbit which further substantiates my claim as well as the ksh portability you mentioned.

The declare or typeset builtins, which are exact synonyms, permit modifying the properties of variables. This is a very weak form of the typing [1] available in certain programming languages. The declare command is specific to version 2 or later of Bash. The typeset command also works in ksh scripts.

In the Bash manual under section 4.2 Bash Builtin Commands it states:

'typeset'
typeset [-afFrxi] [-p] [NAME[=VALUE] ...]
The 'typeset' command is supplied for compatibility with the Korn shell; however, it has been deprecated in favor of the 'declare' builtin command.