Difference between IFTTT, Stringify, WebCore, Device Handlers and SmartApps

Did you read the complex rules FAQ? It should help (this is a clickable link)

IFTTT, Stringify, and yonomi are rules mechanisms created by three separate companies, and none of these companies are part of SmartThings. However, all three of these have provided some integration with SmartThings.

“Smartapps” are code which runs directly on the SmartThings platform, usually in the SmartThings cloud. Some were created by SmartThings staff, some are created by community developers. Anything which is called “custom code” is not officially supported and runs in the smartthings cloud.

Webcore is a custom smartapp whose author was later hired by smartthings for their own staff.