Agile Feels Different
The most noticeable feeling is the sense of making concrete progress. All of the Agile approaches have an anti-bureaucratic stance that encourages the removal of roadblocks that slow progress. Coupling this with the commitment to release or at least demonstrate the software to users every few weeks or so makes for a team environment in which everyone feels that progress is being made.
Agile also feels different because it really encourages collaborative development, making everyone an integral part of a team in which members actually help each other. Team members communicate a lot more because knowledge is shared around the team and there is a constant underlying conversation that binds the team together. Rather than feeling isolated and pressured, team members know that they're not alone.
Customers and users feel involved in the project. Instead of being a nuisance to be ignored whenever possible, in Agile projects suggestions and ideas from customers and users are welcomed with open arms. Agile teams realize that they don't have a monopoly on good ideas and hence welcome suggestions from users as an easy way of improving the software.