I'm not a lawyer, but in layman's terms:
Subrogation is similar to a right of reimbursement in that for example: YOUR Insurance company pays for your medical bills and/or property damage because the person causing your injuries/damages has no insurance. YOUR insurance company then has the right to pursue that person to get reimbursed. They "step into your shoes" to sue or try to obtain the money you would have gotten to pay for those damages, but your insurer paid them, so they have your right to get the money back they already paid on your behalf.
An assignment is like you giving away or assigning the right to collect some amount due to you in the future. Such as when a doctor is about to treat you and you sign an assignment that the doctor will file and collect directly from your health insurer, rather than you pay the bill and submit it to your health insurer and wait for them to hopefully reimburse you for the money you paid.
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