There are three main mute/solo modes in Logic that can act independently if you wish.
1. You have note/region mute (which is "M") this allows you to mute regions within a track or notes within a region. The resulting region or note will be a grey colour to signify it has been muted.
Note: The Mute tool (from the Tool menu) is the same as pressing "M".
2. Then you can mute the track (in the Track Header of the Arrange using the mute button) which gives a "slow response" mute and doesn't use much in the way of system resources.
3. Finally you have the Channel mute (in the Mixer). Muting a channel strip using the mute button provides a "fast" mute but uses more system resources to do so.
You can choose to disable Slow response mute in:
Logic Pro > Preferences > Audio [General]
Either way, you'll still be able to use the Mute tool to quickly mute selected regions, notes within an Arrangement. I find it realy useful to quickly audition changes in an Arrangement to see if I like the part or not and also during the mixing stage I'll use the Solo tool ("S") more frequently too.