Finding the Site template details which is used for a site or a page in SharePoint

Save the current site as site template[.STP extension].

Now, save it to disk somewhere.

Now, navigate to that location and rename the file to .CAB extension.

Extract the CAB file and find the manifest.xml file.

Now, in the file check for the TemplateID string and get the value. 

Please find the List of TemplateId's details:

Site template ID to Name mapping:

0 - GLOBAL (SetupPath=global) - "Global template"
1 - STS - "windows SharePoint Services Site", "Team Site", "Blank Site", "Document Workspace"
2 - MPS - "Basic Meeting Workspace", "Blank Meeting Workspace", "Decision Meeting Workspace", "Social Meeting Workspace", "Multipage Meeting Workspace"
3 - CENTRALADMIN - "Central Admin Site"
4 - WIKI - "Wiki Site"
7 - BDR - "Document Center"
9 - BLOG - "Blog"
20 - SPS (OBSOLETE) - "SharePoint Portal Server Site"
21 - SPSPERS - "SharePoint Portal Server Personal Space"
22 - SPSMSITE - "Personalization Site"
30 - SPSTOC (OBSOLETE) - "Contents area Template"
31 - SPSTOPIC (OBSOLETE) - "Topic area template"
32 - SPSNEWS (OBSOLETE) - "News area template"
33 - SPSNHOME (SubWebOnly) - "News Home template"
34 - SPSSITES - "Site Directory area template"
36 - SPSCOMMU (OBSOLETE) - "Community area template"
38 - SPSREPORTCENTER - "Report Center Site"
39 - CMSPUBLISHING (SetupPath=SiteTemplates\PUBLISHING) - "Publishing and Team Collaboration Site"
40 - OSRV (SetupPath=SiteTemplates\OSRV) - "Shared Services Administration Site"
47 - SPSPORTAL - "Corporate Intranet Site"
50 - SRCHCEN - "Search Center"
51 - PROFILES - "Profiles"
52 - BLANKINTERNETCONTAINER - "Internet Presence Web Site"
53 - BLANKINTERNET - "Publishing Site", "Press Releases Site", "Publishing Site"
54 - SPSMSITEHOST - "My Site Host"
90 - SRCHCENTERLITE (SetupPath=SiteTemplates\SRCHCENTERLITE) - "Search Center Lite"
6221 - PWA (SetupPath=SiteTemplates\PWA) - "Project Web Access Site"
6215 - PWS (SetupPath=SiteTemplates\PWS) - "Project Workspace"
14483 - OFFILE - "Records Repository", "Records Repository"