Both represent separate legal entities.
Main differences are:
by Guarantee | by Shares |
Usually non-profit organisations. | Profit oriented organisations |
No share capital, but members are contributing to cover organisation's debts | Share capital. In other words, individuals risk to lose only share purchase amount. |
Due to nature of the organisation, no dividends to members. Only salary to employees. | Salary to employees. Dividends to shareholders. |
If you are limited by guarantee and wish to re-register to be limited by shares, please follow the link https://www.gov.uk/government/publications/re-register-an-unlimited-company-as-a-limited-company-rr06
Another useful link: https://www.gov.uk/guidance/model-articles-of-association-for-limited-companies