As a general rule no they are not the same, but there's often a little overlap and this is going to depend on the consulting firm and how they scope out the engagement or the client and the specific business need. I've been a consultant / pentester for years and most of the time external pentests and application pentests are different or at least separately undertaken to ensure a deep dive discovery.
I can understand where the confusion can come into play since both assessment types can be externally facing but generally a network pentest is going to focus on the underlying infrastructure and bypassing your perimeter defenses. It may leverage a an application for information or to be used for exploitation but that is not the sole purpose. Focuses may include password attacks, weaknesses in firewall/IDS/VPN, insecure/exposed services, authentication attacks, access to sensitive systems etc...
Application assessments focus on compromising the application itself. It's a deeper dive into the actual applications workings and may include code analysis, authentication bypasses, privilege escalation, injection (SQL injection, XSS, etc...), API testing, database testing, mobile app testing, and subverting application logic.