How do you see growth product manager versus a business development or pure sales roles ? Differences and Similarities ?

I see them as partners working together for a common goal to help grow the company. The main difference is that they each have their own responsibilities that contribute to this common goal.  

• Sales Manager - their responsibility is to directly engage with the customers to close deals. 
• Business development (BD) - is usually responsible for making new partnerships where 1+1=3. 
• Growth PM - is responsible make the features that support smooth onboarding, referrals, discounts etc. 

Analogy (best i can think of right now) - We are a real estate developer with a goal to sell multiple homes we've built

• Sales - they bring potential buyers of our house (the product)
• BD - they find gardening vendors so that we can charge you an HOA fee
• Growth PM - they build the electronic signing documents, and keyless entry lock to insure buyers have a smooth transaction 

I think it depends on the company. If both are doing a similar job, they may have different titles depending on the company.

Eventually a pure sales role is about selling a product, with all the process of negotiating contracts, etc. - while a PM acts on influencing the team to improve business.