Partial vs. Full
When there are changes on OSPF or IS-IS network, all routers in the area/domain would run SPF calculation. SPF calculation is CPU intensive, to reduce the CPU usages on routers, sometimes partial SPF are ran instead of a full SPF.
What is partial SPF? Partial SPF means the SPF tree remains intact, only the leafs of the tree were have changes. For OSPF, when an external route changes. For IS-IS, when a single IP subnet changes.
IS-IS treats all IP subnets as leaf on its SPF tree. A link failure to an IP subnet does not require full SPF recalculation. All IS-IS needs to do is to look for any IS (router) that is directly connected to the lost IP subnet, and moved the IP subnet (leaf) to the IS (router). If there is no IS that is connected to the IP subnet, the subnet will be removed from the IS-IS topology table.
Because of this feature, it is not always bad design to redistribute routes into OSPF as external routes because external routes are considered leafs in OSPF SPF.
Partial vs. Incremental
What is the main different between partial and incremental SPF? Partial is a much simple SPF calculation, it just involves leafs, no links are changed. That menas the SPF tree remains the same after a partial SPF.
As for Incremental SPF, the SPF tree will be changed to discover alternative best path after a link failure. The farther the incremental SPF is ran from the root of the tree, the more saving in time compare to a full SPF. If the change is close to the root, there is little performance improvement over full SPF.