Here's a comprehensive list of all changes. Replace "drupal" with "backdrop" (or case-equivalent) where expected:

Public functions:
The ~250 functions from https://gist.github.com/quicksketch/7077150 all wrapped individually, including class methods.

Private functions:
No replacements provided for private functions.

_drupal_decode_exception
_drupal_exception_handler
_drupal_log_error
_drupal_error_handler
_drupal_error_handler_real
_drupal_schema_initialize
_drupal_shutdown_function
_drupal_default_html_head
_drupal_http_use_proxy
_drupal_css_aggregate
_drupal_build_css_path
_drupal_flush_css_js
_drupal_html_to_mail_urls
_drupal_session_open
_drupal_session_close
_drupal_session_read
_drupal_session_write
_drupal_session_destroy
_drupal_session_garbage_collection
_drupal_session_delete_cookie

Variables:

The "drupal_" prefix on all of these are just dropped, since they universally are not needed and are non-public anyway. They'll also be converted to config before release.

drupal_css_cache_files => css_cache_files
drupal_stale_file_threshold  => stale_file_threshold
drupal_js_version_query_string => js_version_query_string
drupal_js_cache_files => js_cache_files
drupal_private_key => private_key
drupal_weight_select_max => weight_select_max

Constants:

Below aliased directly to BACKDROP_ equivelents.*

Below manually redefined because their files are not loaded early enough.

Globals:
For testing only and not public, so it's not wrapped.

drupal_test_info => backdrop_test_info

Classes and Interfaces:

All wrapped with compatibility mode.

Javascript:

All wrapped in compatibility mode.

Drupal.behaviors.*
Drupal.attachBehaviors()
Drupal.settings.*
Drupal.ajax.*
Drupal.t()
etc.

Libraries:

Using drupal_add_library() with drupal.* works with compatibility mode.

drupal.ajax => backdrop.ajax
drupal.batch => backdrop.batch
etc.
Introduced in branch: 
1.0.x
Introduced in version: 
1.0.0
Impacts: 
Module developers
Theme developers