When we talk about consulting or professional services, we're most often talking about services provided by external vendors and partners.
Consulting and professional services are, essentially, any time a person provides a service based on their skill, experience, or knowledge. For strategy, design, and governance firms, with the exception of a handful of deliverables, the bulk of their "product" is consulting or professional services.
A content management system or web tool vendor may offer value-add services — professional services — in addition to their product. Some vendors use the term solution to refer to the combination of their software and the services surrounding it. Their “solution offering” is often a bundle of licenses to use their software and professional services in the form of integration or consulting.