Conceiving an issue is one of the first steps in determining its legal ruling. Unless something is readily apparent, there is quite a bit of room for differences in conception. Differences in how an issue is conceived lead to differences in how it is judged.
Many of the things we do today have an identical counterpart in classical fiqh. Some of the things we do can be identified as a composition of individual transactions. Others, though, appear to be novel.
For example, scholars differ in how they conceive the relationship between banks and their account holders: are the accounts holders lending the bank money or are they investing in the bank?
Those who consider it a loan view what one receives from the bank as unlawful interest, yet most who hold this view consider still it permissible to deal with banks out of necessity or need.
Those who consider it a form of investment see it as either a form of rectifiable invalid partnership or a completely novel transaction. In both cases, what one receives from the bank is permissible.
While there is an agreement that riba is unlawful, there is disagreement over when what one receives from the bank is riba, or something else. The root of this disagreement is differences in the conception of the problem itself.