Actually, both are similar and carry the meaning of "persuade" or "force." In the Longman Dictionary both patterns (with infinitive and V-ing) appear under the same entry:
- to persuade or force someone to do something
get somebody to do something: I’ll get Terry to check the wiring for me. We couldn’t get him to sign the agreement.
get somebody doing something: In the end, we got the children clearing the playground.
The use of V-ing suggests that an action (barking, in your example, and clearing, in the example above) was caused to start and then continued (durative action). Instead, the use of the infinitive may refer to a short action with an immediate effect, as is the case with check and sign above.