On top of the given answers, the type of referral will also factor in.
When you're up for renewal and go to a comparison site (in the UK: CompareTheMarket, MoneySupermarket, Confused, GoCompare, ... ) and struggle accurately through all their lists of questions, you see that some of the data differs (e.g., not all the same jobs can be entered; if you have had an accident, not all ask whose fault it was and/or don't leave the option "not yet resolved" --possibly forcing you to guess which way it will be adjudicated,-- and/or what the total repair cost was).
So as these referrers feed slightly different data to roughly the same set of insurance providers, you will get slightly different quotes on the same providers. And expect your own provider to offer a slightly better quote than you'll get in reality for renewing: The referrer's (one-time) cut has to be still taken off, but they count it as a new client so somebody gets a bonus for that --- you they disregard as a captive client and give what boils down to a loyalty penalty. [Case in point: I had an unresolved car accident, resolved months later in my favour. With all honest data including unresolved claim and its cost and putting my 'accident-free years' factor at 0 instead of 7, my old provider quoted about 8% more than the previous year on comparison sites; but my renewal papers quoted me 290% more, upon telephone enquiry the promised to refund the difference if court found in my favour though they refused to give this in writing. So: No thanks!]
Then the other set of referrals they get is from you directly going to their website asking for a quote. They know what type of link you've followed (banner, or google result, etc), they may know some info from your browser's cookies (time spent where) or other tracking service, and from your data they may guess how tech-savvy and shop-wise you are, and scale your offer accordingly. [Comparison-site shoppers are lumped together at a relatively high savvy-level, of course!].
Companies breaking down your data and their own in a particular way can find advantages and hence offer you better terms, as said in the main answer (this is like Arbitration in stock exchanges, ensuring a certain amount of sanity: if there's something to exploit, somebody will, and everybody will follow). It may be that they find a certain group of people maybe more accident-prone but cheaper to deal with (more flexible in repair-times, or easy to bully in accepting shared-fault when they weren't at fault), or they want a certain client (for women, for civil servants, for sporty drivers, for homeowners --- often for cross-selling other insurance services). Or they claim to want pensioners because the company can offer them 'a familiar voice' (same account manager always contacting them) while they're easier to bamboozle and less likely to shop around when offered a rubbish deal.
Also, 100% straight comparison of competing offers isn't possible as the fine details of the T&Cs (terms & conditions) would differ, as well as various little pinpricks in the claims handling process.
And depreciation of a car, and various ways of dealing with it: You insure it for the buying prices, but two years later it's worth about 40% less on paper --- so in case of total loss, replacing like-for-like will cost you still at least 80% of the value for which you've been insuring it while they'll probably offer you the 100-40= 60%. Mostly because instead of your trusted car you have something unknown that may have hidden defects, or been mistreated and about to die. [Case in point: My 3-y-old dealer-bought car's gearbox died just outside the 6month warranty period, notwithstanding its "150-item inspection you can rely on". In the end the national brand agreed to refund the parts (15% of what I paid for the car) but not the labour (a few hours).]
And any car model's value differs (in descending order) from its "forecourt price", "private selling price", "part exchange price", and "auction price". Depending on your ompanies may happily insure you for forecourt price (=what you paid to dealer) but then point out that the value of that car is the theoretical P/X value, i.e., the car without anybody's profit, far less than you've been paying for. [Conversely, if you crash it after insuring below market value, they can pay you your stupidly low figure.]