Each Record Type should have it's own Sales Process showing the stages that are appropriate for that type. This video walks through the steps in Salesforce Lightning for making modifications in the Object Manager and in the Sales Process settings for this special type of picklist
The full playlist provides an introduction to Record Types and shows how to build and modify Sales Processes and Sales Paths along with creating new Record Types
Salesforce Lightning Record Types 101.1 Intro – https://youtu.be/w_wdAmyN6lI
Salesforce Lightning Record Types 101.2 Default Profiles –
Salesforce Lightning Record Types 101.3 Record Layouts – https://youtu.be/Woor3peY2ds
Salesforce Lightning Record Types 101.4 Sales Process – https://youtu.be/oX2F9rzycYM
Salesforce Lightning Record Types 101.5 Sales Path – https://youtu.be/t0uNJdvdJcQ
Salesforce Lightning Record Types 101.6 Create New – https://youtu.be/Gx5DOCC7cEM
Salesforce Lightning Record Types 101.7 Updating Picklists