Recaptcha - is it safe/good practice using same site key in different apps

I have an API that has many different clients. In login process I mandate a captcha test on back end, so I require a captcha response from the client.

Is it OK to share the same site key for all my clients? Or should I provide a different site key and secret key tuple per client type, and maintain a dictionary of app id to secret on my back end in order to decipher the response per site?