Can you please explain the difference between PBX and soft switch in less technical terms?

In this day and age you cannot directly compare a soft switch to a PBX. A soft switch, or software that connects phone lines with one another, is at the core of all modern PBXs. Asterisk is not a PBX but it can be configured to function as one. Also most of the functions provided by an PBX can also typically be performed by a class 5 soft switch. Perhaps an example will help clear things up.

A telephone exchange is a system that allows telephone lines to be connected (bridged) to one another. If you pick up your phone in your house and dial your neighbor's home phone (assuming you are both using the local phone company) the telephone company's exchange detects the digits you dial and if you dialed your neighbors phone number connects your phone to your neighbors. You two can now talk and plan your next block party.

Now what if you wanted to pick up your phone in your kitchen and dial a number which rings a phone in your bedroom? One option is to order two phone lines from your phone company, install one in your kitchen and the other in your bedroom, and use their exchange to connect them just like when calling your neighbor. Another option is to install your own exchange, a private branch exchange (PBX), that would allow you to pick up the phone in the kitchen and dial an extension which will ring and connect to the phone in the bedroom without using the phone companies exchange.

Connecting phone lines together is what a PBX does at it's most basic level. Which is the same thing a soft switch does. Except that a PBX can do it either with custom hardware as was the case before general purpose computers were so prevalent or purely in software as modern PBXes and soft switches do today.

Custom hardware is only needed depending on the type of telephone network(s) you need to connect to. If all your endpoints are IP based like SIP phones or softphones and your outside connectivity is provided over the internet like Vonage, Skype, or SIP trunks your PBX only needs a network adapter to bridge them and not any specialized telephony hardware. On the other hand if you have analog endpoints like the typical residential phones you might have in your kitchen and bedroom you would need hardware that can detect if the handsets are on or off hook, generate the voltage to cause a ring and digitize the sound. Likewise if your outside connectivity is via copper wires from your phone company you would need custom hardware in order to bridge the endpoints (IP-based or analog) of your PBX to the phone network.

A PBX (Private Branch Exchange) is a device to switch calls between telephones. Some like Asterisk support VOIP (Voice Over IP). When I looked at implementing Asterisk a few years ago, I found I was looking at a hefty hardware expense for the phone interfaces.

FreeSWITCH is a VOIP switch and handles switching calls between VIOP endpoints (connections). The switch is implemented in software and may not have any physical phones connected to it. Calls may be switched to softphones (software phones) on PCs, laptops, or other devices. Another option is to redirect the call to an existing cell phone or landline (hardwired phone). Some softswitch software can ring several numbers at once and may allow you to listen in to the incoming voice mail message before accepting the call.

A softswitch may allow very complex call routing plans based on who is calling, time of day, and other factors. Follow-me routing should be simpler to implement with a softswitch.

Both may include IVR and voicemail (although it is more or less standard on softswitches).

For many purposes they can be considered interchangeable, but the technological lead is likely to favor the Softswitch.