I have an older heat pump and a/c unit usually works fine today we realized that the blower motor does not shut off.I even turned the thermostat to off but it still runs. Can anyone give me any ideas?Also smelled a little burnt electrical smell when we noticed the blower was not shutting off.

Yep, the contactor to the blower stuck. Needs to be replaced.

The blower motor was just replaced a month ago would that have been replaced then?

Nope.

Its true it may just be a stuck blower relay but that will not explain the burnt smell. You may have a electrical short at the heat strips or blower control wires causing the blower to run all the time. A slight ground can make a 230 volt motor run with out tripping the breaker or fuse. Be careful if you investigate. Turn power off to the system first.

Actually it could explain the smell. If the contacts are heating up, the relay itself can smell.

True but in my opinion I have found that less than 5% of the time the burning smell coming from a residential system is not derived from the blower relay.