ER Modeling; multiplicity basics - one to many or many to many? Apologies for a basic question, but I’m having difficulties determining the multiplicity constraints for a database I’m trying to design.

Our team undertakes a number of services/projects...each involve (at least one) activity (prototyping, evaluations, design). The database is intended to record details of each project we complete, and which activities were used in a particular project (plus other details).

Now, down to my confusion:

In one sense, it is a one to many relationship (1..1  1..*); each project involves at least one and possibly multiple activities.

But, if considering it from a different perspective, it is a many to many relationship (0..* 1..*); an activity could be in the database that is never used in any project on record, and, the same activity could be undertaken in multiple projects (for example, multiple projects could involve ‘design’).

Which perspective is correct?

Kind regards,
Mitch
I think your design could be stated more formally as:

One company has many projects. 
One project belongs to one company.
One project has one or more activities.
One activity has exactly one activity type (prototyping, design).
One activity belongs to exactly one project. 


So, if that's true, you have the following tables:

COMPANY
CompanyID
....

PROJECT
ProjectID
....

ACTIVITY_TYPE
ActivityTypeID
Name (e.g. "Prototyping", "Design")

ACTIVITY
ActivityID
ProjectID
ActivityTypeID
StartDate
EndDate
...