Master Page: The main template where all the common/shareable things like html controls( for footer, header and navigation),CSS, JS files.We could have only one master page for each sharepoint site.
Page Layout: Basically it contains the HTML controls,CSS and JS files which are only specific for creating look and feel for specific pages, and it inherits look and feel from master page.We can have multiple page layouts for site.
Master pages and page layouts dictate the overall look and feel of your SharePoint site. Differences are Master pages contain controls that are shared across multiple page layouts, such as navigation, search, or language-preference for multilingual sites. Page layouts contain field controls and Web Parts Page layouts can be used by all page instances that are based on that page layout. Master pages can be used by all page instances in a site. Page Layout also migrate to the next level version successfully since its using html
Master Page: provides a consistent layout and appearance (look and feel) for SharePoint sites. They allow you to factor out layout, structure, and interface elements such as headers, footers, navigation bars, and content placeholders.Page layout : dictates the overall look and feel of a web page.It relies on a content type to determine the kind of content that can be stored on pages. Page layout contains field controls and web part.