By default, PuTTY has always announced its terminal type to SSH (and Telnet) servers as xterm, and tried to behave close enough to xterm itself that this works well enough.
PuTTY also supports some terminal control sequences not supported by the real xterm: notably the Linux console sequences that reconfigure the colour palette, and the title bar control sequences used by DECterm (which are different from the xterm ones; PuTTY supports both).
Since PuTTY was new, the xterm terminal type has split into many subtypes, so you may find that you benefit from upgrading to a terminal type such as xterm-256color to enable more features.
In modern versions of Linux, the terminal type database also includes a terminal type for PuTTY itself, so you could try setting the terminal type to ‘putty’! We didn't write that database entry, and don't know in detail what it includes or which version of PuTTY it was based on.
(We are sometimes asked why PuTTY doesn't use the ‘putty’ terminal type as default. Part of the reason is inertia. Another is that all the world's not Linux: I still worry that some servers will be confused by that terminal type. But perhaps one day we should switch over.)