Nowadays, message switching is implemented at application level and it is actually transported by packet switching at the network level.
The most common example of this is email: an email is the message, the emails servers are the switches. The email is transferred using store and forward technique between each email servers, through SMTP protocol.
Between two email server, this message is divided into packets that are transported using TCP and IP protocols and pass through several IP networks. Each of this network can contain several switches and routers.
On a single path, the packets may traverse switches that use store and forward as well as other switches that use cut-through switching.
Since different packets may take different paths, you can have for a single message (email) some packets that will traverse some cut-through switches and other packets that will not encounter a single one.
Edit following comments:
Store and Forward vs Cut-Through is the way a specific switch behave. It is not a characteristic of a message / packet.
As stated by @Ron Maupin in comment you can use both technique with either message or packets.
The difference between message switching vs packet switching (in today's network) is that they don't happen at the same level.
They are not of the same nature and doesn't require the same treatment.
In the case of email messages, a small delay is not important, but the integrity of the message is critical. So a store and forward technique is much more appropriate, so each intermediate switch can check the integrity of the message before passing it to the next.
If you care more about speed than about integrity, then you can use cut-through switching. I don't have a good example in mind right now except for audio/video message that doesn't fit well here.
Note that if the message is sent to a network you don't control, or traverse such network, you cannot know how the intermediate switches are configured to behave. Once again in the case of email, it is likelt that all email servers will use S&F but it may traverse an anti-spam / anti-virus gateway that use some kind of cut-through.
The same logic apply for packet switching, but it happen at a different level.
A difference in packet switching is that the packet may be treated differently depending on its content.