Weed or unruly plant?

Hey all, my new to me garden is absolutely crawling with this purple flowered plant. It’s growing like a weed! There seems to be two versions, maybe slightly different but the one in the photos is soft, the other one grows kinda bushy but is sticky. I’m wanting to know what it is so I can either help manage it, or rip it out. Google hasn’t been much help of course.

Also would appreciate any info on the red flowered shrub thing. No idea what it is, but looks nice!