Both are on the member record, and they answer different questions.
Membership history is the record of changes to the membership itself: joining, approval, becoming active, renewals, level changes, suspension, resignation, closure, lapsing, reinstatement, overrides and auto-renew changes. Each row shows When, What happened, the Status before and after where it changed, and By: the staff member, or System for automatic changes such as a lapse. Where a reason was given, it shows under the entry as "Reason:".
Timeline is everything that happened with the member, newest first. It includes payments, renewals, level changes, review decisions on renewal answers, and every email sent to them, such as renewal notices. For an email, click Show the email exactly as it was sent to to read the message they received.
Use Membership history to see why a status changed and who changed it. Use Timeline to see what the member was sent or did.
Changes that need wider oversight, such as overrides, suspensions and closures, are also written to the organization's audit log, which Org admins can see.