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The contextual menus can change based on different layer types. It looks like your first screenshot is from a text layer and the second screenshot is from a Smart Object.
You can also quickly access the Blending Options in the Layer Styles panel by double-clicking on the layer (in the empty space to the right of the thumbnail and name of the layer) in the Layers panel or by going to Layer > Layer Style > Blending Options...
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I also just double-checked the Keyboard Shortcut options. Even though there isn't a keyboard shortcut for Layer > Layer Style > Blending Options..., you can set one by going to Edit > Keyboard Shortcuts... and setting the Shortcuts for Application Menus. Then in the Application Menu Command list below that dropdown menu, twirl open Layer and go to Layer Style > and down to Blending Options... Then enter a keyboard shortcut/combination that isn't currently in use.