The dovetail bar (sometimes called a rail) is one of the great ideas in small telescope design. With the clamp on the mount and a bar on the tube, telescopes (OTAs) and mounts can be readily swapped. However, there are some things that will limit the interchangeability of OTAs and mounts.
First, consider the match of payload of the clamp and mount with the weight of the OTA and accessories. You can easily overload a mount even if the OTA fits perfectly in the clamp.
Second, the scope may have balance issues when used with another mount even if the dovetail and clamp mate well. This is often the case when the new combination is close to or exceeds the payload capacity of the clamp and or mount. The imbalance can affect mount tracking and GOTO performance.
Third, Celestron mounts (and other brands as well) often have moldings or bezels on parts of the mounting around the clamp that are designed for one or just a few OTAs. You might not be able to get the bar deeply enough in the clamp to be securely held on the mount. In these cases, the bezel or molding will need to be removed, modified or replaced to allow safe use of the mount with your OTA.
Fourth, the clearance between the OTA and the mount needs to be considered. While a short tube will generally work on a mount designed for a longer tube, the converse is not true. You can’t mount a Newtonian OTA like the 130 SLT on an SE mount without it colliding with the mount. Areas of the sky above a certain altitude will be inaccessible and must be avoided by the mount though proper use of slew and filter limits.
Finally, all mounts will have a preferred orientation of the tube in the clamp or on the mount. Some mounts have clamps at the top, meaning they work best with OTAs having dovetails on the bottom of the tube. Others have clamps that are either right or left of the OTA when in use.
For example, consider a scope designed and normally used with the OTA mounted so the mount arm is to the right of the tube as seen from behind. The dovetail bar on the scope is thus on its right side and it is considered "right-handed." The mount’s motions expect the tube to be positioned this way as well. Though the tube's dovetail bar will fit many other mounts, the tube may not have this right-handed relationship to the mount. Your finderscope and focusing knob may not be optimally placed for observing convenience with other mounts.
Here is a table of popular Celestron models and their preferred orientations.
CGEM & DX
German equatorial mounts with dovetail bars (AstroMaster. Omni) are bottom oriented. Some models have tube rings – these are bottom oriented and the scope can be rotated to a convenient orientation within the rings.
Spotting scopes with dovetail bars that are also designed to be photo tripod mounted are bottom oriented. This includes the C90 and C-5 spotters.