The reputation of a social entity is a viewpoint about that entity held by others, normally an outcome of social examination. It is very important in commerce, education, online neighborhoods (website reputation), and many other areas.
The word reputation comes from the Latin "reputare" which in English means to reflect or think over. It also comes from the Latin term "reputatio" which translates in English to "pondering over."
Character comes from the Greek word xaraktḗr, which translates in English to "engravers tool."
Reputation is a reflection of the way someone or something is perceived by a community or by individuals. It is the public estimation of how an entity is perceived, not how it truly is.
Put another way, reputation is a reflection of the sentiment held toward the person or entity. Sentiment is an opinion, attitude, or belief. Reputation (repute) is, therefore, an estimation of merit, standing, status, or achievements.
When you say something has a good reputation you believe it to be a true estimation of its character, yet you do not know if it is true. This is because the repute of something is merely an opinion, whereas character is a description of actual qualities and attributes.
Reputation and character are different. The "repute" of an entity (person or thing) is the estimation of how a person or community feels (their sentiment) about a person's character. Character is a combination of actual traits the entity bears.
Another way of looking at it is that character is how a person is, whereas reputation is how a person seems. The character of a thing or person can be completely different from its reputation. Character is far less flexible than reputation.
As mentioned above, reputation and character are different. The reputation of a thing is changeable in nature, whereas character is less so. Because people tend to follow the advice of strangers, for example by trusting online reviews, reputation can be managed. But the character of a brand or company is the soil out of which reputation grows. If the character of a company or person is negative, reputation will eventually, inevitably, follow. But if the character of a person or brand is positive, reputation can be improved and stabilized.