What is the difference between high assurance and low assurance certificates?

Certificate assurance is the level of user trust. It always depends on the certificate validation type and information about the applicant and the company that will be provided to the Certificate Authority (Comodo). The more certificate is engaged in the company verification process, the higher the certificate assurance is.

All SSL certificates are divided into three types: DV (Domain Validation), OV (Organization Validation) and EV (Extended Validation).

Domain Validation (DV) SSL certificates are low and medium assurance ones. The Certificate Authority (Comodo)  should check the domain ownership and ability of the certificate applicant to manage the domain before issuing an SSL certificate. The process of domain name verification is called Domain Control Validation (DCV).
This process is fast enough and takes up to 15 minutes. Low and medium assurance certificates provide the same encryption level and are not limited in any way. The only difference is that low assurance certificates can be used mostly for blogs or personal websites, while medium assurance certificates are commonly used for small volume e-commerce websites.

Low assurance certificates are: PositiveSSL, PositiveSSL Multi-domain and PositiveSSL Wildcard.
Medium assurance certificates can be found here: EssentialSSL, EssentialSSL Wildcard.

High assurance SSL certificates are Organization Validation (OV) ones. To issue such a certificate, the applicant is required to complete the DCV process. After that, the Certificate Authority should verify the legal and physical existence (address and phone number) of the company  applying for the certificate.
The process may take up to 2 business days. These certificates are good for medium and large-volume e-commerce websites.
High assurance certificates can be checked here: InstantSSL, InstantSSL Pro, PremiumSSL, PremiumSSL Wildcard, Unified Communications and Multi-domain SSL.

Extended Validation (EV) SSL certificates provide the very high assurance level. For the certificate issuance, it is necessary to complete the DCV process, pass legal and physical existence verification and submit required documents to the Certificate Authority (Comodo). The validation process may take from 2 up to 10 business days.
These certificates are the best solution for large-volume e-commerce websites, large companies and organizations. Only EV certificates provide a green bar with the company details in the address line of the browser.
The list of very high assurance certificates: EV SSL and EV Multi-domain SSL.