@async vs message queue difference

I have a spring boot project, deploying in two servers and using nginx. One method in the project will do:

1. set some key-values in redis

2. insert something in db

After 1, I want to do 2 in async way.

One solution is to let doDB() be a springboot @async method:

Class A {    public void ***() {        doRedis() // 1.set some key-values in redis        doDB() // 2.insert something in db    }}Class B {    @async    doDB()}

Another solution is to send message to MQ:

Class A {    public void ***() {        doRedis() // 1.set some key-values in redis        sendMessage()     }}Class B {    onMessage(){        doDB()    }}

If Class A and B are both in the spring boot project, just deploying this project in two servers. I think using @async is enough, there is no need to use MQ to achieve the async way because there is no difference between server one to do Class B doDB() and server two to do Class B doDB(). If class B is in another project, then using MQ is good because it's decoupling for project one doing redis work and project two doing db work.

Is it right? Thanks!