The prior poster is missing the L7 tier, which is Senior Staff Engineering Manager for the Engineering Manager Ladder.
L8 is a Director on the Engineering Manager Ladder L8 is a Principal on the Software Engineer (SWE) Ladder.
Tech-Lead Managers (TL/M or TLMs) were on the SWE Ladder.
For reference:
Software Engineer Ladder
L8 - Principal Software Engineer
L7 - Senior Staff Software Engineer
L6 - Staff Software Engineer
L5 - Senior Software Engineer
L4 - Software Engineer II
L3 - Software Engineer (new graduates would start here)
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L2 and below exists in rare occasions.
Engineering Manager Ladder
L8 - Director
L7 - Staff Engineering Manager
L6 - Engineering Manager (M1)
L5 - Engineering Manager (M0 - normally this level does not exist for external hires and is for the rare situation when a SWE is converting to the Engineering Manager ladder)