Adventitious literally means out of place. This is purely for us humans - the plant is doing just fine, thank you, because it evolved to reproduce vegetatively and well as sexually. You can create adventitious roots at home by cutting an herb stem with a few leaves on it off, and placing the cut-off piece into a glass of water. This is called rooting.
You can induce rooting with stolons or with runners by burying them or cutting them off from the parent and doing the glass of water trick.
So they really are very similar. Plant anatomy has a slightly different viewpoint. It deals with the origin - the tissues from which a structure developed - of structures like stolons and runners. If I recall correctly - stolons arise from the cambium in the stem, and runners arise from axillary buds (or the meristem in the bud, more correctly).
The point is the what differentiates them not what they look like, or whether they have roots. but where they arise. Either can create roots - either can break off from the parent to form an independent plant. Sometimes this feature kinda runs amok and you get dangling "babies" Chlorophytum - spider plant:
Sorry about the advertisement - this is the only one I could find showing "babies":
http://www.joann.com/28in-spider-plant/7856081.html?mkwid=x0sHCDie|dc&utm_source=google&utm_medium=cpc&utm_term=&utm_campaign=Shopping+-+Home+Decor&CS_003=12310478&CS_010=[ProductId]&gclid=Cj0KEQjw9JuuBRC2xPG59dbzkpIBEiQAzv4-G_cIIulLf_SfdrNOV2oNbNaFsnlkcpBH4IfjeZC-F18aAv-U8P8HAQ
Chlorophytum:
https://en.wikipedia.org/wiki/Chlorophytum_comosum
So this plant has a kind-of "stolon-runner" which does not fit the definition about stolons having roots.
Actually these definitions are great for starters but, darn it, plants in the real world cannot read Botany books. So they do all kinds of weird things.