The term “theistic evolution” is used in contrast to the atheistic idea of evolution. It means evolution set in motion by God  or under the direction of God , and seems appropriate for a believer who admits some truth to evolutionary science. But I don’t like the phrase because it’s a confusing redundancy.
Think about it. If you’re a believer, it’s already implied that you see all biological and physical processes as created and held in existence by God. You don’t need “theistic” in front of biological terms. Who speaks of theistic reproduction? Or theistic gestation, theistic meiosis, or theistic menstruation? Plus, to qualify a biological process as “theistic” implies that the opposite is possible, that God may not be involved in creating certain laws of nature.
Just leave the unnecessary adjective out. Treat evolutionary science as science. Refuse to treat it as anything else. Judge it on its scientific facts or lack of facts. Such realism clarifies a significant point: True science is objective. Truth is like that. Whatever is scientifically true is theologically true.
If our current knowledge seems contradictory, it’s because we are discursive creatures  not in possession of full knowledge. We search systematically. Science and theology are, by necessity, complementary searches. We don’t need to put boundaries around God or use science to shore up our faith.
Call it a mother’s touch applied to science and theology, but (as I’ve said before ) science ought to be viewed like cooking. Both are human endeavors to discover properties of matter and manipulate those laws to produce something, be it polyelectrolytes or pepperoni pizza. Believers and non-believers can cook in the same kitchen and gather round the same table to enjoy the fruits of their labor. Sure, the grateful believer asks the Lord to bless his meal, but the atheist can observe the object of gratitude too. No one calls the process by which food gets on the table “theistic gardening” or “theistic baking” either.
Richard Dawkins called the term “theistic evolution” an attempt to “smuggle God in by the back door ,” and he was right. God doesn’t need us to do that. Be confident that God, who became Incarnate, makes Himself known through His creation. When we gather to assess and critique evolutionary science, the believers will praise God for his handiwork and the atheists will do whatever they do.
To grasp this confidence and clarity is to grasp why science doesn’t draw a rational person away from religion. In fact, science, like a good meal shared among friends, can even draw a searching mind closer to his Maker.